LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


ELEMENTARY  TEXT-BOOK 


STEAM  ENGINES  AND  BOILERS. 


FOR  THE  USE  OF  STUDENTS  IN  SCHOOLS 
AND  COLLEGES. 


J.    H.    KINEALT, 

Professor  of  Mechanical  Engineering,  Washington  University, 
St.  Louis,  Mo. 


ILLUSTRATED  WITH  DIAGRAMS  AND  NUMEROUS  CUTS 

SHOWING  AMERICAN  TYPES  AND  DETAILS 

OF  ENGINES  AND  BOILERS, 


FIFTH  EDITION. 


NEW  YORK  : 
SPON  &  CHAMBERLAIN,  123  LIBERTY  STREET. 

LONDON  : 
E.  &  F.  N.  SPON,  57  HAYMARKET,  S.  W. 

1905. 


GENERAL 


COPYRIGHT,  1901, 

BY 
J.  H.   KINEALT. 


THE  BURK  PRINTING  HOUSE, 
NEW  YORK. 


PREFACE. 

This  book  is  written  solely  as  an  elementary  text-book 
for  the  use  of  beginners  and  students  in  engineering,  but 
more  especially  for  the  students  in  the  various  universities 
and  colleges  in  this  country. 

No  attempt  has  been  made  to  tell  everything  about 
any  one  particular  subject,  but  an  attempt  has  been  made 
to  give  the  student  an  idea  of  elementary  thermodynamics, 
of  the  action  of  the  steam  in  the1  cylinder  of  the  engine,  of 
the  motion  of  the  steam  valve,  of  the  differences  between 
the  various  types  of  engines  and  boilers,  of  the  genera- 
tion of  heat  by  combustion,  and  the  conversion  of  water 
into  steam. 

Care  has  been  taken  not  to  touch  upon  the  design  and 
proportion  of  the  various  parts  of  engines  and  boilers  for 
strength  ;  as,  in  the  opinion  of  the  writer,  that  should 
come  after  a  general  knowledge  of  the  engine  and  boiler 
has  been  obtained. 

In  the  derivation  of  some  of  the  formulae  in  thermo- 
dynamics, it  has  been  necessary  to  use  the  calculus,  but 
the  use  of  all  mathematics  higher  than  algebra  and 
geometry  has  been  avoided  as  much  as  possible. 

An  earnest  endeavor  has  been  made  to  present  the 
subject  in  a  clear  and  concise  manner,  using  as  few  words 
as  possible  and  avoiding  all  padding. 

J.  H.  KINEALY. 

WASHINGTON  UNIVERSITY, 
August y  1895. 

(iii) 


180712 


PREFACE  TO  THE  FOURTH  EDITION. 

This  edition  is  practically  the  same  as  the  previous  one. 
The  only  change  made  has  been  to  correct  some  typo* 
graphical  errors. 

J.    H.   KlNEALY. 

BOSTON,  MASS., 
August, 


TABLE    OF    CONTENTS. 


CHAPTER  I. 

ELEMENTARY   THERMODYNAMICS. 
ARTICLES. 

1.  Thermodynamics • 

2.  First  Law  of  Thermodynamics        ...... 

3.  Work,  Power • 

4.  Unit  of  Heat 

5.  Mechanical  Equivalent • 

6.  Application  of  Heat  to  Bodies 

7.  Second  Law  of  Thermodynamics  . 

8.  Specific  Heat 

9.  Absolute  Temperature •        • 

10.  Application  of  Heat  to  a  Perfect  Gas     . 

11.  Isothermal  Expansion • 

12.  Adiabatic  Expansion 

13.  Fusion 

14.  Vaporization  

15.  Application  of  Heat  to  Water        ...... 

16.  Superheated  Steam 22 


CHAPTER  II. 

THEORY   OP   THE    STEAM   ENGINE. 

17.  Theoretical  Heat  Engine 23 

18.  Cycle • 

19.  Thermodynamic  Efficiency       . 

20.  Perfect  Gas  Engine 0        27 

21.  Perfect  Steam  Engine 0        .        32 

22.  Theoretical  Diagram  of  the  Real  Engine        .        ...        86 

23.  Clearance •        • 

24.  Efficiency  of  the  Actual  Engine      .        .        .        .        •        -        46 


Vi  STEAM   ENGINES   AND    BOILERS. 


CHAPTER   III. 

TYPES   AND   DETAILS    OF   ENGINES. 

ARTICLES.  PAGE. 

25.  Classification  of  Engines                                                  ,  .        53 

26.  Plain  Slide  Valve  Engines       .......        65 

27.  Automatic  High  Speed  Engines  56 

28.  Corliss  Engines                                                             0        0  „        59 

29.  Cylinder  and  Valve  Chest  61 

30.  Piston 63 

31.  Cross-head 64 

32.  Connecting  Rod        ........  0        68 

33.  Crank        .                 72 

34.  Main  Bearings 74 

35.  Eccentric           ........        0  „        75 

36.  Governors         ..........        76 


CHAPTER  IV. 

ADMISSION   OF    STEAM   BY  VALVES. 

37.  Opening  and  Closing  the  Ports  by  the  Valves        .  ,        „        78 

38.  Relative  Movements  of  the  Piston  and  Valve  83 

39.  Balanced  Slide  Valve 89 

40.  Piston  Valve             90 

41.  Multiple  Admission  Valve  91 

42.  Meyer  Valve     ..........        91 

43.  Corliss  Valve            ......        .  ,        .        92 

44.  Link  Motion  95 


CHAPTER  V. 

VALVE    DIAGRAMS. 

45.  Zeuner  Valve  Diagram  .        .        .        .        .        .        .97 

46.  Valve  Diagram  Problems 101 

47.  Effect  of  the  Obliquity  of  the  Connecting  Rod  on  the  Point 

of  Cut-off          ..........      110 

48.  Swinging  Eccentrics 113 


CONTENTS.  Vll 


CHAPTER  VI. 

INDICATOR   AND   INDICATOR   CARDS. 

ARTICLES.  PAGE. 

49.  Indicators           ....                   .  118 

50.  Adjustments  and  Connections  of  Indicators      .  120 

51.  Reducing  Motions      .  122 

52.  Cord  for  Indicator     .  127 

53.  Taking  the  Indicator  Card                             .  128 

54.  To  Determine  the  Horse-power  from  the  Indicator  Card        128 

55.  To  Find  the  Ratio  of  Clearance  of  the  Engine  from  the 

Indicator  Card    .  .  .  132 

56.  To  Find  the  Weight  of  Steam  used  per  Hour  per  Horse- 

power         ...  .... 

57.  Interpretation  of  the  Action  of  the  Valves  from  the  Ap- 

pearance of  the  Indicator  Card        ....        134 


CHAPTER  VII. 

COMPOUND   ENGINES   AND    CONDENSERS. 

58.  Compound  Engines 

59.  Tandem  Compound  Engines      . 

60.  Cross- Compound  Engines 

61.  Ratio  of  Cylinders  of  Compound  Engines 

62.  The  Horse-Power  of  Compound  Engines  .  145 

63.  Condensers 

64.  Effect  of  the  Condenser  on  the  Power  of  the  Engine        .         150 

65.  Amount  of  Condensing  Water  Required     ....         153 


CHAPTER  VIII. 

HEAT   AND   COMBUSTION   OF   FUEL. 

66.  Steam  Making    .                                                         •  155 

67.  Steam  Required  per  Hour         .  157 

68.  Heat  Required  per  Hour    .  .158 

69.  Fuel  Required  per  Hour     .  •                  160 

70.  Air  Required  for  Combustion     .                           •  I66 

71.  Rate  of  Combustion 

72.  The  Furnace 169 


STEAM   ENGINES    AND   BOILERS. 

ARTICLES.  pAaE 

73.  Firing  the  Furnace 171 

74.  Mechanical  Stokers        ......  174 

75.  Hawley  Down-Draft  Furnace        ....  177 


CHAPTER   IX. 

BOILERS. 

76.  Types  of  Boilers 180 

77.  Old  Types  of  Boilers 181 

78.  Return  Fire-Tube  Boilers 183 

79.  Water-Tube  Boilers 189 

80.  Vertical  Boilers 192 

81.  Marine  Boilers 194 

82.  Rating  of  Boilers 194 

83.  Appendages  to  a  Boiler        .......  196 

84.  Settings  of  Boilers        ....  207 


CHAPTER  X. 

CHIMNEYS. 

85.  Chimneys 212 

86.  Draft    of   Chimney 214 

87.  Velocity  of  the  Gases  Passing  Through  the  Chimney        .        217 


APPENDIX. 

CARE    OF   BOILERS. 

How  to  Prevent  Accidents 221 

How  to  Save  Fuel 224 

How  to  Lengthen  the  Life  of  the  Boiler  225 


TABLES. 

I.  The  Properties  of  Steam  * 229 

II.  Hyperbolic  Logarithms 234 

III.  Factors  of  Evaporation 235 

IV.  Heating  Power  of  Fuels 236 


CHAPTER     I. 

ELEMENTARY     THERMODYNAMICS. 

I.  THERMODYNAMICS. —  The  Science  which  treats  of  the 
laws  and  principles  according  to  which  work  may  be  con- 
verted into  heat  andy  conversely \  heat  into  work  is  Thermo- 
dynamics. 

The  whole  science  is  based  upon  the  present  conception 
of  "  heat  as  a  mode  of  motion  ;  "  and  until  the  present 
theory  of  heat  was  established  and  accepted,  the  science 
was  unknown.  Up  to  about  the  middle  of  the  nineteenth 
century  the  usually  accepted  conception  of  heat  was  that 
it  was  a  material  substance  that  could  be  made  to  enter 
or  leave  bodies;  and  according  as  this  substance  was 
present  in  greater  or  less  quantities  the  body  was  more  or 
less  hot. 

In  1798,  Count  Rumford  was  led  to  assert  that  heat 
was  a  mode  of  motion  and  not  a  material  substance,  by 
the  results  of  experiments  made  while  boring  cannons. 
The  results  of  his  experiments  and  his  conclusions  as  to 
the  nature  of  heat  were  given  in  a  paper,  read  before  the 
Royal  Society  in  England,  entitled,  "An  Enquiry  Con- 
cerning the  Source  of  the  Heat  which  is  Excited  by 
Friction," 

In  1/99,  Sir  Humphrey  Davy,  by  a  series  of  experi- 
ments upon  the  heating  effect  of  rubbing  two  pieces  of 
ice  together,  supported  and  strengthened  the  conclusions 
reached  by  Count  Rumford. 

In  spite,  however,  of  the  work  of  Rumford,  Davy,  and 
others  who  followed  them,  it  was  not  until  about  1843 


2  STEAM   ENGINES    AND    BOILERS. 

that  the  modern  conception  of  heat  as  a  mode  of  motion 
was  firmly  established,  and  accepted  by  physicists. 

To  Dr.  Jules  Robert  Mayer,  of  Heilborn,  Germany,  and 
Dr.  James  Prescott  Joule,  of  Manchester,  England,  is  due 
more  than,  perhaps,  to  any  others,  the  honor  of  firmly 
establishing  the  modern  conception  of  heat.  Dr.  Mayer 
published,  in  1842,  an  essay  on  the  subject,  in  which  he 
showed  by  clear  reasoning  and  analysis  that  heat  could 
not  be  a  material  substance.  This  was  almost  immedi- 
ately followed  by  the  publication,  in  1843,  of  the  results 
of  the  elaborate  experiments  made  by  Joule  at  Man- 
chester. The  results  of  Joule's  experiments  proved 
conclusively  the  falsity  of  the  materiality  of  heat,  and 
established  the  modern  conception. 

In  February,  1850,  Prof.  John  Macquorn  Rankine 
read,  before  the  Royal  Society  of  Edinburgh,  a  paper, 
treating  of  thermodynamics,  which,  with  a  paper  by  Prof. 
R.  Clausius  read  in  the  same  month  and  year,  before  the 
Berlin  Academy,  may  be  considered  as  the  beginning  of 
the  work,  carried  on  since  then  to  the  present  day,  upon 
the  Science  of  Thermodynamics.  It  is  to  be  noted  as  a 
curious  coincidence  that  Rankine,  in  Scotland,  and 
Clausius,  in  Germany,  each  working  independently  of  the 
other,  had  reached  practically  the  same  conclusions  at 
the  same  time. 

Before  leaving  this  subject  it  may  be  well  to  call  attention 
to  the  fact  that  many  of  the  methods  of  discussion  used 
in  thermodynamics,  in  its  application  to  the  study  of  heat 
engines,  are  due  to  Sadi  Carnot,  who,  while  rejecting  the 
modern  conception  and  accepting  the  materiality  of  heat, 
did  much  work  that  has  been  of  value  in  formulating 
methods  of  discussion  and  analysis.  To  him  is  due  the 
idea  of  the  cycle  process  known  as  the  Carnot  Cycle,  a 
discussion  of  which  will  be  given  in  the  proper  place. 

2.  FIRST  LAW  OF  THERMODYNAMICS. —  Work  and  heat 


ELEMENTARY    THERMODYNAMICS.  3 

are  mutually  convertible;  and  whenever  work  is  produced 
by  heat  the  quantity  of  heat  consumed  is  exactly  propor- 
tional to  the  amount  of  work  done,  and,  conversely,  by  the 
expenditure  of  the  same  amount  of  work  the  same  quantity 
of  heat  may  be  produced. 

The  first  part  of  this  law  was  established  by  the 
experiments  of  Rumford  and  Davy,  but  it  was  not  until 
the  careful  experiments  of  Joule  were  made  that  the 
second  part  was  assured. 

/ 

3.  WORK,  POWER. —  Work  is  the  overcoming  of  resist- 
ance. 

In  order  that  work  may  be  done  it  is  necessary  that 
there  should  be  not  only  a  force  but  motion  also.  This 
must  be  kept  clearly  in  mind ;  and  it  must  also  be 
remembered  that  the  element  time  does  not  enter  at  all. 
A  man  may  hold  up  a  weight  for  any  length  of  time 
imaginable,  but  he  does  no  WORK,  in  the  mechanical  sense 
of  the  word,  so  long  as  the  weight  is  held  at  rest.  If, 
however,  he  raises  the  weight,  and  in  so  doing  overcomes 
the  resistance  due  to  the  force  of  gravity,  he  does  work. 
Again,  if  two  men  carry  the  same  weight  of  goods  up  the 
same  stairs,  each  will  do  exactly  the  same  amount  of 
work,  even  if  one  should  carry  his  weight  up  the  stairs  in 
one-tenth  the  time  that  the  other  does. 

The  unit  of  work  is  the  foot-pound  (ft.-lb.),  which  is 
the  amount  of  work  done  by  a  body  in  moving  throzigh  a 
distance  of  one  foot  against  a  resistance  of  one  pound. 

It  follows,  from  the  definition  of  the  unit  of  work,  that 
the  work  done  by  a  body  in  overcoming  any  resistance  is 
equal  to  the  product  of  the  mean  force  of  resistance  and 
the  distance  moved  through.  The  force  must  be  ex- 
pressed in  pounds,  and  the  distance  in  feet.  Since,  then, 
work  is  the  product  of  two  factors  it  may  be  represented 
on  a  diagram  as  the  area  of  a  closed  figure,  whose  mean 
altitude  represents  the  mean  force  of  resistance,  and  whose 


4  STEAM   ENGINES   AND    BOILERS. 

length  represents  the  space  or  distance  moved  through. 
Such  a  figure  may  be  termed  a  "  Work  Diagram." 

To  illustrate  the  method  of  forming  a  "  Work  Dia- 
gram," let,  in  Fig.  I,  OX  and  OYbe  two  lines  drawn  at 
right  angles  to  each  other,  termed  axes,  a  represents 
the  position  of  a  body  that  is  doing  work.  Its  distance, 
ad,  from  OX,  represents  the  force  against  which  it  is  act- 
ing ;  and  its  distance,  aet  from  0  Y,  represents  the  distance 
it  has  moved  from  its  starting  point  or  origin.  Now 


Fig.  l. 

suppose  the  body  moves  from  a  to  b  along  the  line  ab, 
which  is  so  drawn  that  at  any  instant  the  distance  of  the 
body  from  OX  represents  the  force  against  which  it  is  act- 
ing at  that  instant,  and  its  distance  from  0  Frepresents  the 
distance  from  its  origin  at  the  same  instant.  When  the 
body  gets  to  b  it  is  acting  against  a  force  represented  by 
the  line  be;  and  it  has  moved  a  distance  dc  from  a.  The 
work  done  while  the  body  moved  from  a  to  b  is  the  mean 
force  of  resistance,  Fm,  multiplied  by  the  distance  dct  and 
is  represented  by  the  area  of  the  figure  abed. 

If  the  force  of  resistance  had  been  uniform,  while  the 
body  moved  from  a  to  b,  the  line  ab  would  have  been 
parallel  to  OX,  and  the  work  would  have  been  equal  to 
ad  X  dc. 


ELEMENTARY    THERMODYNAMICS.  5 

In  general,  the  expression  for  the  work  done  is  given 
by  the  equation, 


(1) 


Where  F  is  the  force  of  resistance  at  any  instant,  and 
s  is  the  distance  from  the  origin.  In  order  to  solve  (i) 
it  is  necessary  to  know  the  law  of  the  path,  ab,  of  the 
body. 

Power  involves  the  element  time,  and  is  the  amount  of 
work  done  in  a  unit  of  time. 

In  all  calculations  relating  to  engines,  the  power 
involved  is  usually  so  large  that  the  unit  of  power  used  is 
the  Horse-Power,  H.  P.,  which  is  33,000  ft.-lbs.  of  work 
done  in  one  minute  ',  or  550  ft.-lbs.  in  one  second. 

To  obtain  the  Horse-Power  exerted  by  an  engine,  get 
the  work  done  per  minute  and  divide  by  33,000;  or,  if 
W  represents  the  work  done  per  minute,  the  horse-power 
is 

<2>  *•* 


4.  UNIT  OF  HEAT.  —  Rankine  defines  the  unit  of  heat  as 
"the  quantity  of  heat  which  corresponds  to  an  interval  of 
one  degree  of  Fahrenheit's  scale  in  the  temperature  of 
one  pound  of  pure  liquid  water,  at  and  near  its  tempera- 
ture of  greatest  density  (39.1°  Fahrenheit)." 

Other  writers  define  it  as  "  the  amount  of  heat  required 
to  raise  the  temperature  of  one  pound  of  water  from  32° 
to  33°  F." 

In  this  work,  however,  the  Unit  of  Heat  will  be  taken 
as  the  amount  of  heat  required  to  raise  the  temperature  of 
one  pound  of  water  from  62°  to  63°  Fahrenheit. 

The  difference  between   the  three   amounts    taken  as 


6  STEAM    ENGINES    AND    BOILERS." 

the  unit,  is,   however,  so  small  that  in  practice  it  may  be 
neglected. 

5.  MECHANICAL  EQUIVALENT. —  The  "  Mechanical  Equiv- 
alent" means  the  number  of  foot-pounds  of  work  that  is 
done  when  one  unit  of  heat  is  consumed,  and  is  generally 
designated  by  the  letter  J. 

The  experiments  made  by  Rumford  and  Davy  were 
too  crude  to  give  any  accurate  value  for  the  mechanical 
equivalent,  and  it  was  not  until  the  time  of  Mayer  and 
Joule  that  a  value  could  be  assigned  to  it  with  any 
degree  of  certainty.  Mayer,  from  certain  properties  of 
gases,  deduced  a  theoretical  value  forj;  but  it  remained 
for  Joule  to  determine,  by  a  series  of  carefully  conducted 
experiments  extending  from  1842  to  about  1850,  the 
value  of /as  772  ft.-lbs.  This  value  was  accepted  and 
used  as  the  correct  one  until  Joule  and  others  showed 
by  later,  and  perhaps  more  carefully  conducted,  experi- 
ments, that  772  was  probably  too  small. 

Recently,  Rowland,  of  Baltimore,  by  a  series  of 
experiments,  in  which  great  care  was  taken  to  guard 
against  errors  of  all  kinds,  showed  the  value  of  the 
Mechanical  Equivalent  to  be  778  ft.-lbs,  the  unit  of  heat 
being  as  used  in  this  work.  It  is  probable  that  778 
ft.-lbs.  is  nearer  the  true  value  of  J  than  772,  and  in  this 
work  778  will  be  assumed  as  the  true  value. 

6.  APPLICATION  OF  HEAT  TO  BODIES. —  Whenever  heat 
is  imparted  to  a  body,  that  is  not  on  the  point  of  chang- 
ing its  state,  two  effects  may  generally  be  observed  : — 

1st.  The  temperature  of  the  body  rises;  its  "sensible 
heat "  is  increased. 

2nd.  The   body  expands ;  its  volume  is  increased. 

There  are  some  exceptions  to  the  general  law  that  the 
body  expands  when  heated,  but  in  all  cases  the  statement 


ELEMENTARY    THERMODYNAMICS.  7 

of  the  law,  as  given,  will  suffice  if  contraction  be  considered 
as  a  negative  expansion. 

When  heat  is  supplied  to  a  body,  a  part  of  the  heat  is 
used  simply  to  increase  its  temperature,  and  the  remainder 
is  converted  into  work.  The  work  done  may  be  classed 
under  two  heads,  internal  and  external.  The  internal 
work  is  made  up  of  two  parts:  the  first  is  the  work 
done  in  effecting  that  change  of  the  condition  of  the 
particles  due  simply  to  the  increase  of  temperature ;  the 
second  is  the  work  done  in  increasing  the  volume  of  the 
body  against  the  resistance  of  molecular  attraction.  The 
external  work  is  that  due  to  the  increase  in  the  volume 
of  the  body  against  the  resistance  of  the  pressure  of  the 
surrounding  air  or  gases. 

The  general  expression  for  the  heat  used  in  heating  a 
body  may,  then,  be  put  in  the  form 

(3)  H  =  JQ  =  S  +  L  +  W. 

H  is  the  total  heat  used,  expressed  in  mechanical  units, 
i.  e.,  foot-pounds  ;  /is  the  Mechanical  Equivalent  of  heat, 
778  ;  <2  is  tne  total  heat  used,  expressed  in  heat  units ;  »S 
is  the  heat  used  in  simply  increasing  the  temperature  of 
the  body ;  L  is  the  heat  used  in  doing  the  internal  work ; 
W  is  the  heat  used  in  doing  external  work.  S,  L,  and  W 
are  expressed  in  foot-pounds. 

7.  SECOND  LAW  OF  THERMODYNAMICS. —  Rankine  gives 
this  law  as  follows  :  "  If  the  total  actual  heat  of  a  homo- 
geneous and  uniformly  hot  substance  be  conceived  to  be 
divided  into  any  number  of  equal  parts,  the  effects  of  those 
parts  in  causing  work  to  be  performed  are  equal" 

He  also  says,  "  This  law  may  be  considered  as  a  par- 
ticular case  of  a  general  law  applicable  to  every  kind  of 
actual  energy ;  that  is,  capacity  for  performing  work  con- 
stituted by  a  certain  condition  of  each  particle  of  a  sub- 


8  STEAM    ENGINES    AND    BOILERS. 

stance,  how  small  soever,  independently  of  the  presence 
of  other  particles  (such  as  the  energy  of  motion)  ." 

Rankine's  statement  of  the  Second  Law  means  simply 
that  a  unit  of  heat  is  equivalent  to  a  definite  amount  of 
work  independent  of  the  part  or  the  temperature  of  the 
hot  body  from  which  it  is  taken.  A  unit  of  heat  taken 
from  the  inside  of  a  body  is  equivalent  to  the  same 
amount  of  work  as  a  unit  of  heat  taken  from  the  surface ; 
and  a  unit  of  heat  from  a  body  whose  temperature  is 
1000°  is  exactly  the  same  as  a  unit  of  heat  taken  from  a 
body  whose  temperature  is  60°. 

Clausius  agrees  with  Rankine  in  his  statement  of  the 
first  law,  but  as  his  method  of  reasoning  is  different  from 
that  of  Rankine,  his  statement  of  the  Second  Law,  or 
Second  Main  Principle  as  he  calls  it,  is  different.  It  is  : 
"  Heat  cannot,  of  itself,  pass  from  a  colder  to  a  hotter  body" 

8.  SPECIFIC  HEAT. —  There  are  two  specific  heats  to 
every  body ;  they  may  be  termed  the  apparent  specific 
heat,  and  the  real  specific  heat. 

The  apparent  specific  heat  is  the  amount  of  heat  required 
to  raise  the  temperature  of  one  pound  of  a  substance  one 
degree  Fahrenheit. 

The  apparent  specific  heat  is  usually  spoken  of  as 
simply  the  "  specific  heat.  "  It  includes  not  only  the 
amount  of  heat  required  to  change  the  temperature  of  the 
body  one  degree,  but,  also,  that  heat  used  in  doing  such 
internal  and  external  work  as  may  accompany  the  change 
of  temperature.  It  is  further  subdivided  into  specific  heat 
at  constant  volume,  CM,  and  specific  heat  at  constant  pres- 
sure, £p. 

Specific  heat  at  constant  volume  is  the  amount  of  heat 
required  to  change  the  temperature  of  one  pound  of  a 
substance  one  degree  when  the  volume  is  kept  constant.  It 
includes  only  such  heat  as  is  required  for  the  change  of 
temperature  and  that  part  of  the  internal  work  due  to  this 
change,  and  excludes  all  heat  required  to  do  work  on 
account  of  change  of  volume. 


ELEMENTARY   THERMODYNAMICS.  9 

Specific  heat  at  constant  pressure  is  the  amount  of  heat 
required  to  change  the  temperature  of  one  pound  of  a  sub- 
stance one  degree  when  the  pressure  is  kept  constant.  It  in- 
cludes all  the  heat  required  to  do  the  internal  and  external 
work  due  to  change  of  volume,  and  is,  therefore,  greater 
than  the  specific  heat  at  constant  volume. 

The  real  specific  heat  of  a  body  is  the  amount  of 
heat  required  simply  to  change  the  temperature  of  one 
pound  of  a  substance  one  degree,  excluding  all  heat  used 
for  internal  and  external  work. 

In  the  case  of  perfect  gases  the  internal  work  done 
during  a  change  of  temperature  is  zero,  and  the  specific 
heat  at  constant  volume  is  actually  equal  to  the  real 
specific  heat.  In  the  cases  of  solids  and  liquids,  the  amount 
of  heat  used  for  internal  work  when  the  temperature  is 
changed  at  constant  volume  is  so  small  as  compared  with 
that  required  only  for  change  of  temperature,  that  it  is  usual 
to  consider  the  specific  heat  at  constant  volume  as  equal 
to  the  real  specific  heat. 

Let  -£v  represent  the  specific  heat  at  constant  volume, 
expressed  in  foot-pounds  ;  K^  the  specific  heat  at  constant 
pressure,  in  foot-pounds  ;  then,  for  a  perfect  gas, 

(4)  Jp,=,7cp=  7*=14Morair_ 

Ay  J   CV 

9.  ABSOLUTE  TEMPERATURE. — Gay-Lussac  made  a  series 
of  experiments  to  determine  the  change  in  volume  of  a 
gas  when  heated  under  constant  pressure,  and,  as  a  result 
of  his  experiments,  found  that  the  volume,  Ft,  of  a  gas  at 
a  given  temperature,  /,  on  the  Fahrenheit  scale,  was  always 
given  in  terms  of  its  volume,  VQ  ,  at  o°,  and  its  temperature 
/,  by  the  equation 

(5)  Ft  =  F0(l  +  aO, 

where  a  is  a  constant  factor,  equal  to  — ^ — ,  termed  the  co- 
efficient of  expansion  of  perfect  gases. 

*  This  symbol  is  the  Greek  letter  Gamma.  It  is  used  by  all  writers  to  repre- 
sent the  ratio  of  Jfp  to  K^. 


10  STEAM    ENGINES    AND    BOILERS. 

If  the  temperature,  /,  of  the  gas  is  below  zero,  or  nega- 
tive, then  the  plus  sign  in  (5)  becomes  minus. 

If  a  gas  is  cooled  below  o°  its  volume  will  be  less  than 
Vo\  if  the  cooling  is  continued,  and  the  gas  should  always 
contract  in  the  manner  indicated  by  Gay-Lussac,  it  is 
apparent  that  finally  a  temperature  will  be  reached  where 
the  volume  of  the  gas  will  become  zero.  To  determine 
this  temperature  put,  in  (5),  for  V^  its  supposed  value,  and 
get, 

O  =  F0(l+aO.     Whence  t  =  --  -=—461. 

ct 

This  pointy  —  461,  is  the  absolute  zero,  on  the  Fahrenheit 
scale,  and  temperatures  counted  from  it  as  the  starting  point 
are  absolute  temperatures,  and  are  usually  designated  by  T. 

Since  the  absolute  zero  is  461  Fahrenheit  degrees  below 
the  Fahrenheit  zero,  any  temperature,  /,  on  the  Fahrenheit 
scale  may  be  converted  into  a  temperature,  T,  on  the 
absolute  scale  by  adding  461  to  it.  T  =  461  +  t. 

Equation  (5)  may  be  written  in  the  form 


• 

To  is  the  absolute  temperature  for  o°  F.,  and  is  equal  to 
461;  T  is  the  absolute  temperature  for  f  F.,  equal  to 
461  +t. 

Equation  (6)  may  be  changed  to 

(7)  Ir  =  ^  =  a  constant. 

10.  APPLICATION  OF  HEAT  TO  A  PERFECT  GAS.  —  If  a 
pound  of  gas  be  put  into  a  cylinder,  closed  at  one  end, 
in  which  works,  without  friction,  a  piston,  the  gas  will 
expand  and  force  out  the  piston  until  the  pressure  of  the 
gas  inside  the  cylinder  is  equal  to  that  of  the  air  on  the 
outside.  If  now,  while  the  temperature  is  kept  constant, 


x>      •  "7"* 

f  o"  THE 

(UNIVERSITY 

V^  o? 

^^JJ^-'^ 


ELEMENTARY   THERMODYNAMICS.  11 

the  volume  of  the  gas  is  decreased  by  pushing  in  the 
piston,  the  pressure  exerted  by  the  gas  on  the  piston  will 
be  increased ;  if  the  volume  occupied  by  the  gas  is 
increased,  the  pressure  exerted  by  it  on  the  piston  will  be 
decreased.  The  pressure  exerted  by  the  gas,  while  its 
temperature  remains  constant,  will  increase  or  decrease, 
as  the  volume  is  decreased  or  increased,  according  to 
"  Boyle's  Law,"  which  is:  the  pressure  exerted  by  a  gas, 
whose  temperature  remains  constant^  is  inversely  as  its 
volume. 

In  other  words,  if  V\  and  P±  represent  respectively  the 
initial  volume  and  pressure  of  a  gas,  at  a  constant  tem- 
perature, and  V-2  and  P2  its  final  volume  and  pressure,  the 
relation  existing  between  V\,  Pi,  Vi,  and  Pi,  is 

(8)  ZL  =  4X  or  p2  F2  =  Pi  Fi  =  a  constant. 

Fl  /2 

From  equation  (7),  representing  the  relation  between 
the  volume  and  absolute  temperature  of  a  perfect  gas 
under  a  constant  pressure,  and  equation  (8),  representing 
the  relation  between  the  volume  and  pressure  of  a  per- 
fect gas  under  a  constant  temperature,  is  obtained  the 
relation  that  must  always,  under  all  circumstances,  exist 
between  the  volume,  pressure  and  absolute  temperature 
of  a  perfect  gas.  It  is  given  by  the  equation 

(9)  ^p  =  ~p  =  R,  a  constant.   ' 

When  the  pressures  are  expressed  in  pounds  per  square 
foot  and  the  volumes  in  cubic  feet,  the  value  of  R  for  one 
pound  of  air  is  53.15.  For  w  pounds  of  a  gas  the  con- 
stant is  w  R. 

Let  it  be  supposed  that  the  air  in  the  cylinder,  spoken 
of  before,  is  heated,  while  the  pressure  is  kept  constant 
at  PI  Ibs.  per  square  foot,  until  the  absolute  temperature 
is  increased  from  7i  to  7a .  By  definition,  the  amount 


12  STEAM   ENGINES    AND    BOILERS. 

of  heat  supplied  to  the  pound  of  the  gas  is,  in  mechan- 
ical units,  the  change  in  temperature,  T2 —  71,  multiplied 
by  the  specific  heat  at  constant  pressure,  KP)  or 

(10)  H  =  K»(T2  —  Ti). 
But  from  (3)  it  is  evident  that 

(11)  H=S  +  L  +  W. 

Where  S,  the  heat  required  to  change  only  the  temper- 
ature, is,  fora  perfect  gas,  Kv  (T* — 71),  since  the  real 
specific  heat  is  equal  to  the  specific  heat  at  constant  volume; 
L,  the  internal  work,  is,  for  a  perfect  gas,  equal  to  zero ; 
and  W,  the  external  work,  must  be  the  total  force  exerted 
on  the  piston  multiplied  by  the  distance  it  has  moved. 
The  total  force  exerted  on  the  piston  is  the  pressure  per 
square  foot,  Pi,  multiplied  by  the  area,  A,  of  the  piston ; 
and  if  the  initial  distance  of  the  piston  from  the  bottom 
of  the  cylinder  is  d\,  and  the  final  distanc  e  is  d^,  the  dis- 
tance moved  is  di — d\.  The  external  work  is,  then, 

W=PiA  (d2  —  di)  =Pi  (Ad2— Adi). 

But  Adi  is  equal  to  V2,  the  final  volume  occupied  by 
the  gas ;  and  Adi  is  equal  to  V\t  the  initial  volume  of  the 
gas.  The  expression  for  Wis,  therefore, 

Tr=Pi(F2  —  Fi). 
If  for  5,  L,  and  W\  are  put  their  values,  (n)  becomes, 

(12)  H=Kv(T,  —  Ti)  +  Pi(F2  —  Fi) 

=  KV(T2—  Ti)  +  P,  F2  —  Pi  Fi. 

Since  the  relation  between  the  initial,  and  the   final 


ELEMENTARY   THERMODYNAMICS.  13 

pressure,  volume,  and  absolute  temperature  must  satisfy 

P   Vi  PI  V\ 

equation  (9),  we  have     \..    —  R,  and  =  R. 

Whence,         P1  Vz=  R  T^  and  PI  Fi  =  /2  TI 

Substituting  these  values  of  /\  J^  and  /^  f^l  in  (12), 
and  putting  for  .//  its  value,  as  given  by  (10),  there  is 
obtained, 

(13)  #p  (T2  —  TO  =  /rv  <!T2  -  TO  +  R  (T2  —  7\). 

From  which, 


For  a  perfect  gas,  /^*  specific  heat  at  constant  pressure 
is  equal  to  the  specific  heat  at  constant  volume  plus  R% 

ii.  ISOTHERMAL  EXPANSION.  —  A  body  expands  or 
contracts  Isothermally,  when  its  volume  is  increased  or 
decreased  in  such  a  way  that  the  temperature  remains 
constant. 

Since  the  temperature  remains  constant  during 
isothermal  expansion,  the  term  S,  representing  the  heat 
required  to  effect  a  change  of  temperature  of  the  body,  in 
(3)  becomes  zero  ;  and  the  expression  for  the  heat  used 
by  the  body  during  isothermal  expansion  is 

H  =  L  +  W. 

That  is,  all  the  heat  given  to  the  body  is  transformed 
into  work,  part  of  which  is  internal  and  part  external. 

Since,  for  a  perfect  gas,  the  term  Z,  representing  the 
internal  work,  becomes  zero,  as  has  been  stated,  the 
expression  for  heat  becomes, 

11=  W. 
From  the  general  law  of  a  perfect  gas,  expressed  by 


14 


STEAM    ENGINES    AND    BOILERS. 


(9),  it  is  evident  that  if  the  temperature  is  constant  we 
have, 


(15) 


p,2  V?  = 


—  TiR=a,  constant. 


\ 


Fig.  2. 

Equation  (15)  represents  the  law  of  the  change  of 
pressure  and  volume  during  isothermal  expansion  ;  and 
the  curve  represented  by  the  equation,  on  the  work 
diagram,  is  called  the  Isothermal  curve,  which  for  a 
perfect  gas  is  the  equilateral  hyperbola. 

In  Fig.  2  let  OX  and  0  Y  represent  the  two  axes  ;  the 
co-ordinates  of  a,  PI,  V\t  the  initial  pressure  and  volume 
of  the  gas ;  and  the  co-ordinates  of  bt  P%,  Vz,  the  final 
pressure  and  volume  of  the  gas.  Also,  let  the  curve  ab 
be  an  isothermal  curve,  or  equilateral  hyperbola.  The 
work  done  by  the  gas  in  expanding  isothermally  from  V\ 
to  Fz,  is  represented  by  the  area  of  the  diagram  abed; 
and  since  the  heat  used  is  equal  to  the  work  done, 


(16)        H  =  W  =  area  abed  =    \PdV=Pi  Fi    K£ 


r 

l« 

^  Vi 


=  PI   Fi  hyp.  log.  ^r 


*  Hyp.  log.  ifi  the  usual  contraction  for  "  hyperbolic  logarithm."    Table  II  is  a 
table  of  hyperbolic  logarithms. 


ELEMENTARY  THERMODYNAMICS.  15 

12.  ADIABATIC  EXPANSION.  —  Bodies  expand  adiabati- 
cally  when  during  the  expansion,  they  neither  emit  nor 
receive  any  heat.  This  is  expressed  by  making  H  in 
equation  (3)  equal  to  zero,  and  the  equation  then  be- 
comes, 

(17)  0  =  8  +  L  +  W. 
From  which 

(18)  L  +  W  =  —  8. 

For  one  pound  of  the  body  5  is  equal  to  the  specific 
heat  at  constant  volume,  assumed  as  equal  to  the  real 
specific  heat,  multiplied  by  the  difference  between  the 
final  and  initial  absolute  temperatures,  and  (18)  becomes, 

(19)  L  +  W=  —  S  =  —  KV(T2  —  7\)  =/fv  (!Fi  —  T2). 

This  equation  shows  that  during  adiabatic  expansion 
the  temperature  of  the  body  falls  and  that  the  heat  freed 
by  the  fall  in  temperature  is  converted  into  work.  Dur- 
ing adiabatic  compression,  the  work  done  on  the  body  is 
converted  into  heat  which  increases  the  temperature  of 
the  body. 

For  a  perfect  gas  the  internal  work,  Z,  done  during 
expansion  is  equal  to  zero,  so  that  for  a  perfect  gas  (19) 
becomes, 


(20) 


In  order  to  obtain  an  expression  for  the  relation  that 
exists  between  P  and  V  during  adiabatic  expansion, 
assume,  in  Fig.  3,  that  the  curve  abt  termed  an  adiabatic 


16 


STEAM    ENGINES    AND    BOILERS. 


curve,  represents  the    changes  of  volume  and    pressure 
during  expansion   of  one  pound   of  gas;    and    that    the 

Y 


d  c 

Fig.  3. 

area  abed  represents  the  work  done  during  adiabatic  ex- 
pansion. Assume  the  law  of  the  relation  of  P  to  V  to 
be  represented  by  the  equation 

P  Fn  =  P2  F2n  =  Pi  Fin  =  a  constant. 

Where  n  is  an  exponent  whose  value  remains  to  be 
determined.  The  work  done  during  expansion  is  repre- 
sented by  the  area  abed ;  and  by  calculus, 


(21)  areaa&cd:=  W  = 


l-n 


c    & 

*-/  T-T  *S         TT1 


Fi  ~    F1 

Pi  Fi  —  P2  F2 
n-1 


It  is  already  known,  from  (20),  that   the   work    done 
during  adiabatic  expansion  is 


(22) 


ELEMENTARY    THERMODYNAMICS. 


From  (9)  it  is  known  that  71  —  T2  =  PI  Vl  ~ 


17 


R 

Putting  this  value  of  71  —  T-i  in  (22),  we  get  from  (21) 
and  (22), 


(23)  W 

From  this, 


(Pi  Fi  —  P2  F2 


R 


Pi  —  P2  F2 

71-1 


From  (14)  we  have  A"p  =  ^  +  A"v ;  and  from  (4)  we  have 

•^•P  T-I  r  ^P 

•pr  =  7.     Therefore,  ^  =  -77-  =  7. 

Ay  Ay 

The  relation,  then,  between  P  and  F  during  adiabetic 
expansion  is,  since  n  is  equal  to  7, 

(24)          PF7  =  P2  F27  =  Pi  Fi7  =  a  constant. 


Fig.  4. 


18  STEAM     ENGINES     AND     BOILERS. 

A  comparison  of  the  equation  of  the  isothermal  curve 
(15),  with  that  of  the  adiabatic  curve  (24),  makes  it 
apparent  that  the  latter  is  the  steeper  curve. 


A  F2       Pi  Vi 
From    (9)       —  ^  —        —  ^  —  ,  and,  therefore, 


/j     ~     '      T7"     '^      T7  * 
2              Kl             -*2 

Therefore, 
VFij 

^i             /     ^2\  ' 

But               -^1        =    =          (       -y          \    > 

T7"  /\   /7i  5  or 

Kl             ^2 

(25)  ^ 


In  Fig.  4,  let  #^  and  <:</  represent  the  isothermal  curves 
of  a  perfect  gas  corresponding  to  the  absolute  temperatures 
71  and  7a  respectively.  Also,  let  #£  and  ^  represent 
adiabatic  curves  intersecting  the  isothermal  curves.  If 
now  a  gas  expands  so  that  the  relation  between  P  and  V 
is  shown  by  the  adiabatic  curve  ac,  from  71  to  7a,  the 
work  done  will  be,  from  (20),  K^  (71  —  7"2),  and  will  be 
represented  by  the  area  #££/".  Also,  if  the  gas  expands 
according  to  the  adiabatic  curve  bd,  from  71  to  7"2,  the 
work  done  will  be  Kv  (71  —  7i),  and  will  be  represented 
by  the  area  bdnm. 

Therefore,  the  area  acgfis  equal  to  the  area  bdnm. 

By  inspection  of  the  figure  it  is  seen  that,  area  abdc  + 
area  cdng  +  area  acgf  =  area  abmf  +  area  bdnm. 

From  which,  as  area  acgf  =  area  bdnm,  we  get  area 
a£i&  =  area  abmf  —  area  cdng. 

If  the  expansion  were  carried  so  far  that  7a  became  zero, 
the  area  cdng  would  also  become  zero,  and  we  should 
have  area  abdc  =  area  abmf.  When  T%  is  zero,  the  lines 


ELEMENTARY  THERMODYNAMICS.  19 

eg  and  dn  will  be  at  infinity  and  each  equal  to  zero. 
Hence  we  have,  since  acgf  is  always  equal  to  bdnm,  that 
the  work  done  during  adiabatic  expansion  from  Pi  and  T\ 
to  zero  temperature  is  equal  to  that  done  during  adiabatic 
expansion  from  P\  and  71  to  zero  temperature. 

13.  FUSION. —  When  a  solid  body  changes   to   a  liquid 
it  is  said  to  fuse  or  melt. 

The  temperature  at  which  fusion  takes  place,  under 
standard  atmospheric  pressure  of  14.7  Ibs.  per  square  inch 
or  2 1 1 6. 8  Ibs.  per  square  foot,  is  termed  the  fusing  point  of 
the  body.  During  fusion  the  temperature  of  the  solid 
and  liquid  remains  constant  at  the  fusing  point,  so  that  in 
the  general  expression,  H=  S  +  L  +  W,  for  heat  used  by 
a  body,  the  term  .S  becomes  zero.  The  expression  for  the 
heat  to  fuse  one  pound  of  a  body,  is,  then,  H=  L  -f-  W. 

The  heat  required  to  fuse  one  pound  of  a  solid,  under  stand- 
ard atmospheric  pressure,  is  the  latent  heat  of  fusion. 

As  the  change  of  volume  on  fusing  is  small,  for  most 
solids,  the  value  of  W,  the  external  work,  is  small ;  and 
the  greater  part  of  the  latent  heat  of  fusion  is  used  in 
doing  internal  work.  In  the  case  of  bodies,  such  as  ice, 
that  decrease  in  volume  on  fusing,  W  becomes  negative. 

14.  VAPORIZATION. —  Vaporization  is  the  conversion  of 
a  liquid  into  a  vapor. 

The  temperature  at  which  vaporization  takes  place 
depends  not  only  upon  the  liquid  to  be  vaporized,  but,  also, 
upon  the  pressure  to  which  it  is  subjected.  During  the 
vaporization  the  temperature  remains  constant,  if  the 
pressure  does  not  vary. 

The  temperature  at  which,  under  a  given  pressure,  a 
liquid  is  converted  into  a  vapor  is  termed  the  "  boiling 
point "  for  the  given  pressure. 

The  heat  required  to  vaporize  one  pound  of  liquid  under 
a  given  pressure  is  the  latent  heat  of  evaporation  for  the 
given  pressure. 


20  STEAM   ENGINES    AND    BOILERS. 

Since,  during  vaporization,  the  temperature  of  the 
liquid  remains  constant,  the  expression  for  latent  heat  of 
evaporation  is 

H  =  l  =  L+  W. 

As  most  liquids  expand  considerably  upon  being  con- 
verted into  vapor,  the  value  of  Wt  the  external  work,  may 
be  quite  large. 

15.  APPLICATION  OF  HEAT  TO  WATER. —  When  heat 
is  applied  to  water  its  temperature  rises  gradually,  and  as 
the  specific  heat  of  water  increases  slightly  as  the  tem- 
perature rises,  the  heat  required  to  raise  one  pound  of 
water  from  ti  to  fa  is  somewhat  greater  than  fa  — 1\.  For 
ordinary  work,  however,  it  is  sufficiently  accurate  to  assume 
that  the  specific  heat  of  water  is  constant,  and,  therefore, 
that  the  heat,  in  heat  units,  required  to  change  the  tem- 
perature of  one  pound  of  water  from  t\  to  fa  is  fa  — 1\.  In 
mechanical  units  it  is  J  (fa  —  ti).  If  the  heating  is  con- 
tinued long  enough  the  temperature  of  the  water  will  be 
raised  to  the  boiling  point,  and  the  water  will  be  converted 
into  steam. 

The  latent  heat  of  evaporation,  in  heat  units,  of  steam 
is  usually  denoted  by  /,  and  may  be  approximately 
calculated  by  the  equation,  given  by  Rankine, 

(26)  I  =  1114.  4  —  Q.7t. 

t  is  the  temperature,  in  Fahrenheit  degrees,  at  which 
the  steam  is  formed. 

If  (26)  is  multiplied  by  J9  equal  to  778,  there  will  be 
obtained,  llt  the  latent  heat  of  steam  expressed  in 
mechanical  units  : 

(27)  ll==Jl  =  867000  —  544.6*. 


ELEMENTARY  THERMODYNAMICS.  21 

The  heat,  h,  in  heat  units,  required  to  raise  the 
temperature  of  one  pound  of  water  from  h  to  t\  and 
convert  it  into  steam  at  t\  is 

(28)  h=l  +  tl  — 1-2. 

Multiply  (28)  by  J  and  we  shall  have,  h\t  the  heat  in 
mechanical  units  required  to  raise  the  temperature  of  one 
pound  of  water  from  /2  to  t\  and  convert  it  into  steam 
at  /i. 

(29)  hi  =Jh=J[l  +  t1  —  fe]. 

The  latent  heat  is  used  in  doing  the  internal  work  L, 
and  the  external  work  W.  The  external  work  is  the 
product  of  the  pressure  per  square  foot,  under  which  the 
steam  is  formed,  and  the  difference  between  Fw,  the 
volume  of  one  pound  of  the  water  and  Fs,  the  volume  of 
one  pound  of  the  steam.  Assuming  that  Fw  is  so  small 
as  compared  to  Fs  that  it  may  be  considered  as  zero,  and 
that  the  pressure  per  square  inch  under  which  the  steam 
is  formed  is  p,  the  external  work  is,  approximately, 

(30)  TT=144#F8. 

In  practical  problems  relating  to  the  steam  engine  we 
usually  know  the  values  of/  and  A;  but  the  value  of  F3 
must  be  obtained  from  a  table  made  from  the  results  of 
actual  experiments. 

Pressure  gauges,  used  to  indicate  the  pressure  of  steam 
in  steam  boilers,  are  so  constructed  that  they  do  not 
show  the  absolute  or  tme  value  of  the  pressure  of  the 
steam,  but  show  the  pressure,  per  square  inch,  above  that  of 
the  atmosphere.  The  pressure  of  the  atmosphere  is  14.7 
(often  taken  as  15)  pounds  per  square  inch.  In  order, 
then,  to  obtain  the  absolute  value,  /,  of  the  pressure  of 
the  steam  it  is  necessary  to  add  14.7  to  the  gauge 
pressure. 


22  STEAM    ENGINES    AND    BOILERS. 

Tables  giving  the  different  properties  of  steam  for 
different  pressures  are  termed  Steam  Tables  ;  and  are  all 
based  upon  experiments  made  by  Regnault.  Table  I,  in 
this  work,  is  a  Steam  Table. 

In  the  first  column  is  given  the  gauge  pressure,  per 
square  inch,  of  the  steam,  calculated  upon  the  assumption 
that  the  atmospheric  pressure  is  14.7  pounds  per  square 
inch.  The  gauge  pressure  is  given  rather  than  the  abso- 
lute pressure,  as  the  author  considers  it  the  more  conven- 
ient of  the  two  to  use  in  practice. 

In  the  second  column  is  given  the  temperatures,  to  the 
nearest  degree,  in  Fahrenheit  degrees,  of  the  steam 
formed  under  the  different  pressures. 

In  the  third  column  is  given,  in  heat  units,  the  total 
heat  above  32;  i.  e.,  the  total  quantity  of  heat  required 
to  raise  one  pound  of  water  from  32°  to  the  temperature 
of  the  steam,  and  then  turn  it  into  steam. 

In  the  fourth  column  is  given,  in  heat  units,  the  latent 
heat  of  the  steam. 

In  the  fifth  column  is  given  the  volume,  in  cubic  feet, 
of  one  pound  of  the  steam. 

16.  SUPERHEATED  STEAM.  —  When  steam  is  sepa- 
rated entirely  from  the  presence  of  water  and  heated  it 
becomes  superheated,  and  approaches  the  condition  of 
a  gas  ;  the  higher  its  temperature  is  raised  the  more  and 
more  it  departs  from  the  nature  of  a  vapor  and  approaches 
that  of  a  gas.  The  more  nearly  it  assumes  the  condition 
of  a  gas,  the  more  nearly  will  the  equations  of  a  gas 
apply  to  it. 


CHAPTER     II. 

THEORY    OF    THE    STEAM    ENGINE. 

17.  THEORETICAL  HEAT  ENGINE. —  A  heat  engine  may 
be  defined  as  a  machine  for  converting  heat  into  work. 

In  the  theoretical  heat  engine  we  suppose,  what  never 
exists  in  reality,  that  we  have  a  machine  that  works  with- 
out friction  and  that  is  made  of  materials  that  will  act  as 
perfect  conductors  or  non-conductors  of  heat,  as  desired. 
These  suppositions  are  made  in  order  that  the  problems 
may  be  simplified  in  the  beginning.  After  we  have  dis- 
cussed the  theoretical  engine  we  can  discuss  the  real 
engine,  with  its  attending  complications  of  friction  and 
losses  of  heat  by  radiation  and  conduction. 

In  all  engines,  theoretical  or  otherwise,  the  heat  is 
brought  from  its  source  to  the  engine  by  what  is  termed 
the  working  fluid;  this  may  be  a  liquid,  a  liquid  and  vapor, 
or  a  perfect  gas.  In  the  theoretical  engine,  it  is  supposed 
that  all  the  changes  through  which  the  working  fluid 
passes,  during  the  transformation  of  heat  into  work,  take 
place  in  the  engine  itself;  the  working  fluid  is  supposed 
to  always  remain  in  the  engine  and  the  same  portion  of 
the  fluid  is  supposed  to  be  used  over  and  over  again. 

1 8.  CYCLE.  —  The  term    cycle,  as    applied    to   a   heat 
engine,  means  a  number  of  consecutive  scries  of  changes  in 
the  condition  of  the  working  fluid,  such  that  the  final  condi- 
tion of  the  fluid,  at  the  end  of  the  series,  is,  in  all  respects, 
the  same  as  was  the  initial  condition  at  the  beginning  of  the 
series. 

In  every  cycle  three  processes  are  gone  through  :  — 

(23) 


24  STEAM    ENGINES    AND    BOILERS. 

1.  A  quantity   of  heat  is  given  to  the  working  fluid  by 
a  hot  body* 

2.  A  part  of  the  heat  received  by  the  working  fluid  is 
given  to  a  cold  body.  / 

3.  A  part  of  the  heat  received  by  the  working  fluid  is 
transformed  into  external  work. 

As  the  working  fluid  is,  in  all  respects,  in  precisely  the 
same  condition,  as  to  temperature,  pressure,  and  volume, 
at  the  end  of  the  cycle  that  it  was  at  the  beginning,  the 
internal  work  done  during  the  cycle  must  amount  to  zero, 
and  no  heat  can  have  been  used,  therefore,  to  do  internal 
work.  It  follows,  then,  that  the  total  amount  of  heat 
given  to  the  working  fluid  during  a  cycle,  must  be  equal 
to  the  sum  of  that  given  by  the  working  fluid  to  the  cold 
body  and  that  converted  into  work.  Let  H  be  the  total 
quantity  of  heat  received  from  the  hot  body  ;  U  the 
quantity  given  to  the  cold  body  by  the  working  fluid; 
and  W  that  quantity  transformed  into  external  work. 
Then,  if  all  are  expressed  in  mechanical  units, 

(31)  H=  U+  W. 

Equation  (31)  may  be  considered  as  the  principal 
equation  for  the  cycle  of  the  theoretical  heat  engine. 

H  can  usually  be  calculated  when  the  working  fluid 
employed  is  known,  and  when  the  conditions  under 
which  the  heat  is  received  are  known. 

W  can  always  be  obtained  from  the  work  diagram, 
formed  by  plotting  the  various  changes  of  pressure  and 
volume  of  the  working  fluid  during  the  cycle* 

If  is  sometimes  difficult  to  calculate,  but  if  the  working 
fluid  and  the  conditions  under  which  the  cooling  takes 
place  are  known,  there  will  be  no  trouble. 

As  an  example  of  a  cycle,  assume  that  the  co-ordinates 
of  the  point  a  in  Fig.  5  represent  the  pressure  and  volume 
of  one  pound  of  the  working  fluid  of  a  perfect  engine. 


THEORY    OF   THE    STEAM   ENGINE. 


25 


Let  Plt  V\t  and   71,  be  the  initial  pressure,  volume,  and 
absolute  temperature,  respectively,  of  the  fluid. 


Fig.  5.  V 

Suppose  the  working  fluid  is  heated  at  the  constant 
volume  V\  until  the  pressure  is^/2,  and  the  absolute  tem- 
perature is  72.  The  line  ab  will  represent  the  changes  of 
volume  and  pressure  during  this  process. 

Next,  let  the  fluid  receive  heat  at  the  constant  pres- 
sure P2  until  its  volume  is  J/2,  and  its  absolute  temperature 
is  Ts.  be  will  represent  the  changes  of  volume  and  pres- 
sure during  this  part  of  the  cycle. 

Now,  let  the  hot  body  be  removed  and  a  cold  one  be 
substituted  for  it,  and  let  the  working  fluid  be  cooled  at 
the  constant  volume  Vi  until  the  pressure  is  PI,  and  its 
absolute  temperature  is  T±.  cd  will  represent  the  changes 
of  volume  and  pressure  during  this  process. 

Let  the  fluid  be  further  cooled  at  the  constant  pressure 
PI  until  the  volume  is  V\y  and  the  absolute  temperature  is 
71.  When  this  has  been  done,  the  cycle  will  have  been 
completed  and  the  fluid  will  have  arrived  at  its  original 
condition. 

The  heat  given  to  the  working  fluid  is  made  up  of 
two  parts :  — 

I.  That  taken  in  while  being  heated  at  constant  volume, 
equal  ATV  (  71  —  71), 


26  STEAM    ENGINES    AND    BOILERS. 

2.  That  taken  in  while  being  heated  at  constant  pres- 
sure, equal  K^  (  T$  —  T*  ). 
Therefore, 


The  heat  given  by  the  working  fluid  to  the  cold  bod}* 
is  also  made  up  of  two  parts  :  — 

1.  That  emitted    while  being  cooled   at  constant  vol- 
ume, equal  Kv  (  T$  —  T±  ). 

2.  That  emitted  while  being  cooled  at  constant  pres- 
sure, equal  K^  (T±  —  71). 

Therefore, 

U=  Kv  (T3  —  T±)  +  /ip  (T,  —  TO. 

The  external  work  done  is  represented  by  the  area  of  the 

work  diagram  abed 

Therefore, 

W=(P2—  Pi)  (F2—  Fi). 

If  the  values  of  H,  U,  and  Wy  as  derived,  are  substituted 
in  (31),  we  have 

ffv  (T2  —  TO  +  /fp  (Ts  —  T2)  =  Kv  (T3  —  T4)  + 
Kp  (T4  —  Ti)  +  (A  —  A)  (Fa  —  Fi). 

The  changes  that  the  working  fluid  is  supposed  to  pass 
through  during  the  cycle  may  be  any  we  choose.  In  the 
Carnot  cycle,  named  after  Sadi  Carnot,  the  changes 
are  :  — 

1.  The  fluid  receives  heat  while  expanding  isothermally. 

2.  The  fluid  expands  adiabatically. 

3.  The  fluid  is  cooled  while  being  compressed  isother- 
mally. 

4.  The  fluid  is  compressed  adiabatically. 


THEORY    OF    THE    STEAM    ENGINE.  27 

J 

19.  THERMODYNAMIC  EFFICIENCY.  —  This  term  is  used 
to  denote  the  ratio  of  the  work  done  during  a  cycle,  to  the 
total  heat  taken  by  the  working  fluid  from  the  hot  body. 
The  algebraic  expression  for  the  efficiency  is 

w        W  -  U 

E==U~         ~H' 

The  external  work  done  by  a  heat  engine  is  equal  to  the 
product  of  the  heat  used,  H,  and  the  efficiency,  E,  or 
W=  HE. 

As  will  be  seen  later,  the  Carnot  cycle  is  the  most  effi- 
cient of  all  possible  cycles  for  any  working  fluid;  and  the 
expression  for  the  efficiency  of  this  cycle  is 


(33) 


71  is  the  absolute  temperature  at  which  the  working 
fluid  receives  its  heat. 

T-2  is  the  absolute  temperature  at  which  the  working 
fluid  emits  its  heat  to  the  cold  body. 

20.  PERFECT  GAS  ENGINE. —  The  perfect  gas  engine  is 
supposed  to  be  a  theoretical  engine  using  a  perfect  gas 
as  a  working  fluid.  When  a  gas  is  used  as  the  working 
fluid,  all  the  calculations  necessary  to  determine  the  heat 
received  or  emitted  by  the  gas,  during  a  cycle,  can  readily 
be  made,  since  all  the  properties  of  a  perfect  gas  are  well 
known. 

For  instance,  in  Art.  1 8,  it  was  shown  that  for  a  perfect 
engine  using  one  pound  of  any  fluid,  the  expressions  for 
Hj  U,  and  W  for  the  cycle  used,  are 

JF=(P2-Pi)(F2-Fi). 


28  STEAM   ENGINES    AND     BOILERS. 

If  the  fluid   had  been  a  perfect  gas,  it  will  be  easy  to 
show  that  H —  £7=  Wt  as  it  ought. 

To  do  this,  let  us  refer  to  Fig.  5,  remembering  that  for 

PV 
a  perfect  gas  -y  :  =  R,  and  K^  =  Kv  +  R,  and  determine 

the  va.lues  of  71,   T-2,   T3,  and  71,  in  terms  of  P^  V\t  P?, 
and    V* 


Putting  these  values   of  71,  7*,  7J,  and  71,  in  the  ex 
pressions  for  ^T  and  Ut  we  get 


, 


From  (35),  H—  U=  (P2  —  PI)  (Fi—  F2) 


But  -  p  -  =  i,  from  (14),  and,  therefore,  we  have 


THEORY    OF    THE    STEAM    ENGINE. 


29 


proved  algebraically  that 


f  g  m  n 

Fig.  6. 

If  the  cycle  of  work  of  the  perfect  gas  engine  be  the 
Carnot  cycle,  Fig.  6  represents  the  diagram  of  work.  The 
point  a  represents  the  initial  condition  of  one  pound  of  the 
gas,  where  its  pressure  is  Plt  its  volume  Vi,  and  its  absolute 
temperature  71.  During  the  first  period  of  the  cycle  it 
expands  isothermally  from  a  to  b,  where  its  pressure  is  P>2, 
its  volume  Vi,  and  its  absolute  temperature  71.  Next  it 
expands  adiabatically  from  b  to  d,  where  its  pressure  is 
/s,  its  volume  Vs,  and  its  absolute  temperature  Ti.  Then 
it  is  compressed,  and  heat  is  taken  from  it,  so  that  it  con- 
tracts isothermally  from  d  to  c,  where  its  pressure  is  P^ 
its  volume  V\  and  its  absolute  temperature  T-2.  During 
the  last  period  it  is  adiabatically  compressed  from  c  to  a, 
thus  completing  the  cycle. 

While  the  gas  expanded  isothermally  from  a  to  b,  the 


30  STEAM    ENGINES    AND    BOILERS. 

heat  given   to  it  was  that   necessary  to  do  the  external 
work,  represented  by  the  area  abmf,  which,  from  (16),  is 

Pi  Fi  hyp.  log.    -?-.      Therefore, 

(36)  H=Pi  Fi  hyp.  log.  ~. 

v\ 

The  heat  emitted  by  the  gas  to  the  cold  body,  is  equal 
to  the  work  done  during  isothermal  compression  from  d 
to  c,  represented  by  the  area  cdng,  which,  from  (16),  is 

P*    V\  hyp.  log.  ~-    Therefore, 

(37)  U=  P4  Fi  hyp.  log.  -~. 

The  external  work  done  during  the  cycle  is  represented 
by  the  area  abdc.  Area  abdc  =  area  abmf  +  area  bdnm  — 
area  acgf —  area  cdng.  But,  as  has  been  shown  in  Art. 
12,  area  acgf=  area  bdnm,  and,  therefore,  W=  area  abdc 
=  area  abmf —  area  cdng.  Since  area  abmf  =  H,  and 
area  cdng  =  U,  we  get  from  (36)  and  (37), 

(38)  W=  Pi  Fi  hyp.  log.  j^  —  P4   F4  hyp.  log.  ~. 

*  1  K4 

From  (9)  we  have  Pl  V±  =  71  R  and  P±  F4  =  T2  R; 
and  since  ac  and  &/  are  adiabatic  lines,  we  have,  from 

(25), 

M7-1 


From  this  relation  we  get    — -  =  — . 


THEORY    OF    THE    STEAM    ENGINE.  31 


Putting    for  Pi  Fi,  its  value,   71  Rt  for   P^   V±  its   value, 
>  R,  anc 
and  (38), 

(39) 


T7  -rr 

i>  R,  and  for  -JL  its  value,    — 1»  we  have,   from  (  36),  (  37  ), 


H=RTlhyp.  log.   IL. 


U=  R  T2  hyp.  log.  II. 


W=  R  (T!—  T2)  hyp.  log.        2. 

M. 

The  efficiency  of  the  perfect   gas  engine  working  ac- 
cording to  the  Carnot  cycle  is,  from  (39), 


Since  this  expression  for  E  does  not  involve  any  special 
function  or  property  of  the  working  fluid,  we  say  : 

The   efficiency    of  all  heat  engines,  using  any  working 
fluid  according  to  the  Carnot  cycle,  is  as  given  by  (40), 
71  —  T-2 
71     ' 

As  a  further  proof,  let  us  suppose  that  the  perfect  gas 
engine  is  used  to  run  in  the  reverse  direction  a  heat 
engine  using  a  working  fluid  that  is  more  efficient  than 
the  perfect  gas.  The  working  fluid  in  the  second  engine 
would  take  heat  from  the  cold  body  at  a  temperature  T-i\ 
would  have  work  done  upon  it,  instead  of  doing  work  ; 
and  would  give  heat  to  the  hot  body  at  a  temperature 
71.  The  second  engine  is  transforming  work  into  heat 
instead  of  heat  into  work.  It  is  evident,  therefore,  that 
since  the  working  fluid  of  the  second  engine  is  in  pre- 
cisely the  same  condition  at  the  end  of  the  cycle  that  it 
was  at  the  beginning,  the  heat  given  to  the  hot  body 
must  equal  the  sum  of  that  taken  from  the  cold  body  and 
that  resulting  from  the  transformation  of  work  into  heat. 
It  follows  also,  that  if  the  second  engine  is  more  efficient, 


32  STEAM    ENGINES    AND    BOILERS. 

as  supposed,  than  the  perfect  gas.  engine,  it  will  give  to 
the  hot  body  more  heat  than  the  perfect  gas  engine  trans- 
forms into  work.  But  as  all  the  work  done  by  the  perfect 
gas  engine  is  used  to  run  the  second  engine,  the  two  to- 
gether form  a  system  by  means  of  which  heat  is  either 
being  created  or  made  to  pass  from  a  cold  to  a  hot  body 
without  any  disappearance  of  energy  or  change  of  any 
kind  in  the  conditions  of  the  working  fluids.  That  is,  by 
an  arrangement  of  machinery,  heat  is  either  created  or 
made  to  pass  from  a  cold  to  a  hot  body  without  any  com- 
pensation. 

This  conclusion  is  contrary  to  all  our  experience  as  to 
the  action  of  heat,  and  to  our  knowledge  of  the  transform- 
ation of  heat  into  energy,  and,  therefore,  cannot  be  con- 
sidered true.  Hence,  the  second  engine  is  not  more 
efficient  than  the  perfect  gas  engine. 

If  it  were  supposed  that  the  second  engine  ran  the  per- 
fect gas  engine  in  a  reverse  direction,  the  same  argument 
would  show  that  the  second  engine  cannot  be  less  effici- 
ent than  the  perfect  gas  engine. 

We  are,  therefore,  forced  to  conclude  that,  since  the 
second  engine  is  neither  more  efficient  nor  less  efficient 
than  the  perfect  gas  engine,  the  two  engines  have  the 
same  efficiency. 

By  a  method  of  proof  that  belongs  to  a  more  advanced 
work  than  this,  it  can  be  shown  that  the  Carnot  cycle  is 
the  most  efficient  of  all  possible  cycles.  Care  must  be 

taken  to  remember  that  the  efficiency  of  the  heat  engine 

'p  *p 

is  -  : —  only   when  working   according  to  the    Carnot 

T\ 

cycle. 

It  would  be  well  for  the  student  to  work  out  the  ex- 
pressions for  the  work  done  by,  and  the  efficiency  of,  the 
perfect  gas  engine  working  according  to  a  number  of 
the  cycles  given  under  the  head  of  Problems. 

21.  PERFECT    STEAM    ENGINE.  —  The    perfect     steam 


THEORY    OF    THE    STEAM    ENGINE.  33 

engine  is    a  theoretical  engine  using  water  and  steam  as 
the  working  fluid. 

In  the  actual  steam  engine  the  working  fluid  is 
usually  considered  as  being  steam  only.  This  is  due 
to  the  fact  that  the  steam  engine  really  consists  of 
two  parts  that,  in  practice,  are  separated  and  are 
considered  always  as  being  separate  and  apart  from 
one  another.  These  parts  are  the  engine,  proper,  and  the 
boiler.  The  steam  receives  its  heat  while  in  the  boiler, 
from  which  it  passes  to  the  engine  and  there  does  work ; 
then  it  leaves  the  engine  and  usually  passes  out  and  away. 
The  steam  drawn  from  the  boiler  is  replaced  by  an  amount 
of  water  necessary  to  make  a  quantity  of  steam  equal  to 
that  taken  away.  In  some  cases,  the  steam,  after  leaving 
the  engine,  is  condensed  and  returned  to  the  boiler.  In 
such  cases,  the  actual  engine  approaches  nearer  to  the 
perfect  engine  than  in  any  other,  as  here  the  same  work- 
ing fluid  is  used  over  and  over  again.  In  the  perfect 
steam  engine  the  water  is  supposed  to  be  converted  into 
steam  while  in  the  engine,  and  the  engine  itself  takes  the 
place  of  both  engine,  proper,  and  boiler,  in  the  actual 
engine.  The  changes  that  the  steam  passes  through  dur- 
ing one  cycle  of  the  perfect  steam  engine,  may  be  sup- 
posed to  be  exactly  the  same  that  it  would  pass  through 
in  an  actual  engine  and  boiler  together,  if  the  losses  of 
heat  due  to  radiation  and  conduction  are  neglected,  and, 
therefore,  the  work  diagram  of  a  cycle  of  the  perfect 
steam  engine  will  be  the  same  as  the  work  diagram  of 
the  real  engine. 

The  cycle,  then,  that  the  perfect  engine  will  be  assumed 
to  make  will  be  that  which  approaches  nearest  to  the  cycle 
of  the  actual  engine. 

In  Fig.  7,  let  a  represent  the  initial  condition  of  one 
pound  of  water,  just  on  the  point  of  boiling,  whose  volume 
is  Vvr,  pressure  per  square  foot  is  PI,  and  temperature  is 
ti  F.  Let  heat  be  given  to  the  water  so  that  it  will  be  all 

3 


34  STEAM    ENGINES    AND    BOILERS. 

converted  into  steam  at  the  temperature  t\  F.  The  line 
showing  the  change  in  volume  will  be  the  line  ab,  parallel 
to  0 X,  since  the  pressure  remains  constant.  At  b  the 

volume  of  the  steam  will  be  V\,  the  volume  of  one  pound 

p 

of  steam  under  a  pressure  per  square  inch  of .      When 

all  the  water  has  been  converted  into  steam,  let  the  hot 
body  be  taken  away  and  let  the  steam  expand  from  b  to 
d.  In  the  actual  engine  the  line  of  expansion  bd  is  not 
an  adiabatic  line,  but  usually  approaches  nearer  the 
equilateral  hyperbola,  unless  the  expansion  is  great,  whose 
equation  is  PI  V\  =  PI  Vi  =  PV.  We  will  suppose,  then, 
in  order  that  the  cycle  of  the  perfect  steam  engine  may 
approach  as  nearly  as  possible  to  that  of  the  real  engine, 
that  the  steam  loses  some  heat  while  expanding  from  b  to 
d,  and  that  bd  is  an  equilateral  hyperbola.  While  ex- 
panding from  b  to  d,  part  of  the  heat  in  the  steam  is  being 
transformed  into  work,  and  some  of  the  steam  is  being 
condensed  ;  so  that,  at  d  the  fluid  in  the  engine  is  a  mix- 
ture of  water  and  steam  at  a  volume  V*,  pressure  per 
square  foot  PI,  and  temperature  /2°  F.  At  d  it  is  sup- 
posed that  the  engine  is  put  in  contact  with  a  cold  body, 
corresponding  to  the  condenser  of  the  actual  engine,  and 
all  the  steam  is  condensed  at  the  uniform  temperature 
/2°  F.  The  line  showing  the  change  in  volume  during  the 
condensation  is  dc,  parallel  to  OX,  since  the  pressure  is 
constant.  The  point  c  represents  one  pound  of  water, 
whose  volume  is  Vz,  under  a  pressure  per  square  foot  of 
P-2,  and  at  a  temperature  /2°  F.  Now,  the  engine  is 
again  put  in  contact  with  the  hot  body  until  the  tempera- 
ture of  the  water  is  increased  from  fa  to  A,  and  the  pres- 
sure raised  from  P%  to  PI,  thus  completing  the  cycle. 
The  line  ac  represents  the  change  in  volume  and  pressure 
during  this  last  period  of  the  cycle,  and  it  is  sufficiently 
accurate  to  consider  it  as  parallel  to  OY ;  the  volume  at 
c  is  equal  to  the  volume  at  a. 


THEORY    OF    THE    STEAM    ENGINE. 


35 


The  total  quantity,  H,  of  heat  given  to  the  water  dur- 
ing the  cycle  is,  evidently,  the  heat  required  to  raise 
the  temperature  of  the  water  from  h  to  t\t  plus  the  latent 
heat  of  evaporation  at  t\ ;  it  can  be  obtained  from  Table  I, 


m 


Fig.  7. 


in  this  work,  or  it   may  be  calculated   by  using  the  ap- 
proxmate  formulae  given  in  Art.  15. 

The  work,  W,  done  during  the  cycle  is  represented  in 
the  work  diagram  by  the  area  abdc.  From  the  figure,  it 
is  seen  that  area  abdc  =  area  abng  +  area  bdmn  —  area 
dcgm. 

Area  abng  =  Pi  (  Fi  —  Fv). 


Area  bdmn  =     \PdV  =  PiV±      --  =  Px  Fi  /W-  Zo^.  -^ 


Area  dcgm  =  A  (  F2  —  Fs). 


36  STEAM    ENGINES    AND     BOILERS. 

Therefore, 

F> 
W  =  area  abdc  =  PI  (  Fi  —  Fw)  +  PI  Fi  hyp.  log.  -y- 

-P2(F2-  Fa). 

Vw  and  Pa  are  usually  so  small  that  they  may,  without 
error,  be  considered  as  zero,  and  the  expression  for  W 
becomes 


(41)  W  =  Pi  Fi   l  +  fty/>.  log.  ~    -  P2  F2. 

The  value  of  Ut  the  quantity  of  heat  emitted  by  the 
fluid  during  the  cycle,  cannot  be  calculated  directly,  as 
we  do  not  know  the  quantity  of  heat  emitted  during 
expansion  from  b  to  d>  nor  the  exact  quantity  of  steam 
condensed  during  compression  from  d  to  c.  The  value 
of  Ut  however,  is  given  by  the  expression 

U=H—  W. 

The  efficiency  of  the  engine  working  according  to  the 
given  cycle  is, 


P!  Fi  (1  +  hyp.  log.  -^  )-  P2  F2 

(42)         E  =-—  =  ^ - 

H  H 


If  the    engine    had    followed     the    Carnot   cycle     its 
efficiency  would  have  been 


22.  THEORETICAL  DIAGRAM  OF  THE  REAL  ENGINE. — 
In  order  that  all  may  fully  understand  the  explanation  of 
the  action  of  the  steam  in  the  engine,  those  who  are  not 


THEORY    OF   THE    STEAM   ENGINE. 


37 


f          *o 


38  STEAM    EXGIXES    AXD    BOILERS. 

familiar  with  the  names  of  the  different  parts  of  the 
engine  should  refer  to  Figs.  8  and  9. 

The  steam  is  taken  from  the  boiler  to  the  "  steam 
chest  "  of  the  engine,  through  the  u  steam  pipe."  From 
the  steam  chest  it  passes  through  the  "  steam  ports  " 
into  the  "  cylinder,"  and  there  moves  the  "  piston." 
The  motion  of  the  piston  is  communicated  through  the 
"  piston  rod  "  to  the  "  connecting  rod,"  then  to  the 
"  crank,"  by  means  of  which  the  "  crank  shaft  "  is  given 
a  rotating  motion.  While  the  piston  moves  from  one 
end  of  the  cylinder  to  the  other,  makes  one  "  stroke," 
the  crank  makes  half  a  revolution. 

The  "point  of  cut-off"  is  that  point  in  the  stroke  at 
which  the  piston  is  when  steam  ceases  to  be  admitted  to 
the  cylinder:  thus,  the  point  of  cut-off  is  at  one-quarter 
stroke,  if  the  steam  ceases  to  be  admitted  at  the  instant 
the  piston  has  finished  one-quarter  of  a  stroke. 

The  action  of  the  steam  in  the  cylinder  is  as  follows :  It 
begins  to  enter  the  cylinder  when  the  piston  is  beginning 
its  stroke,  and  by  its  pressure  forces  the  piston  forward. 
As  the  piston  moves  forward  steam  is  generated,  at  a 
constant  pressure,  in  the  boiler,  and  flows  into  the  cylin- 
der ;  so  that  the  volume  displaced  by  the  piston  is  kept 
constantly  filled  with  steam  at  the  boiler  pressure.  When 
the  piston  reaches  the  point  of  cut-off  the  valve  closes 
communication  between  the  steam-chest  and  the  cylin- 
der, and  steam  can  no  longer  enter  the  cylinder.  From 
this  on  to  the  end  of  the  stroke,  the  steam  expands  and 
drives  the  piston  forward  simply  by  its  expansive  force. 
As  the  piston  reaches  the  end  of  its  stroke  the  valve 
opens  the  exhaust  port,  and  the  steam  at  once  rushes  out 
of  the  cylinder  into  the  place  of  exhaust,  until  the  pres- 
sure in  the  cylinder  becomes  about  equal  to  that  of  the 
place  into  which  the  steam  is  exhausted.  If  the  engine  ex- 
hausted into  the  atmosphere,  the  pressure  of  the  steam  in 


THEORY    OF   THE    STEAM    ENGINE. 


39 


40  STEAM    ENGINES    AND    BOILERS. 

the  cylinder  would  drop  almost  to  the  atmospheric  pres- 
sure when  the  exhaust  port  is  opened.  In  order  to  empty 
the  cylinder  of  the  steam  remaining  in  it,  the  piston  is 
forced  back  to  its  original  position,  against  whatever 
pressure  there  may  be  in  the  place  of  exhaust,  either  by 
the  pressure  of  steam  admitted  on  the  other  side  of  the 
piston  or  by  the  momentum  of  the  fly-wheel  fixed  to  the 
shaft. 

To  make  the  diagram  of  work  done  by  the  engine 
during  one  forward  and  backward  stroke,  assume,  in  Fig. 
IO,  that  ao  represents  the  absolute  pressure,  Pi,  in  pounds 
per  square  inch,  of  the  steam  entering  the  boiler.  Since 
the  steam  enters  at  constant  pressure  up  to  the  point  of 
cut-off,  the  line  ab  will  represent  the  volume,  V\,  in  cubic 
feet,  of  the  steam  admitted  to  the  cylinder  at  a  pressure 
per  square  foot  of  144  P\. 

From  the  point  of  cut-off  the  steam  expands  until  the 
piston  reaches  the  end  of  the  stroke,  when  the  volume 
of  the  steam  is,  in  cubic  feet,  V^  and  its  pressure  is  P$ 
pounds  per  square  inch,  as  represented  by  the  point  c. 
The  line  of  expansion,  be,  may  be  assumed  as  the  equi- 
lateral hyperbola,  whose  equation  is  P\  T/i=P2  V<z=PV. 

When  the  exhaust  port  is  opened,  at  the  end  of  the 
stroke,  the  pressure  immediately  falls  to  Ps,  as  represented 
at  d. 

On  the  return  stroke,  the  piston  moves  against  the 
constant  "  back  pressure "  Ps,  as  represented  by  the 
line  de. 

During  the  forward  stroke  of  the  piston,  the  steam  does 
the  work  on  the  piston  represented  by  the  area  abcfo; 
and  during  the  return  stroke,  the  piston  does  the  work  on 
the  steam  represented  by  the  area  edfo.  Therefore,  the 
effective  work  done  by  the  steam,  for  each  forward  stroke 
of  the  piston,  is  represented  by  the  area  of  the  diagram 
abcde. 


THEORY    OF   THE    STEAM   ENGINE. 

From  the  figure,  we  see  that 

area  abcfo  =  area  abgo  +  area 
area  abgo  =  144  PI  Fi, 


41 


fF 

L4|pd 

e-/    Fi 


area  bcfg  ==  144  |PdF=  144  PI  Fi    ^/=144P1Fi  hyp.log.~- 


Therefore,  the  work  done  during  a  forward  stroke  is 


(43)       Wi  =  area  a6c/o  =  144  PI    FI  (1  +  hyp.  log.       ). 


Fig.  10. 

If  we  call  Pm  the  mean  forward  pressure  in  pounds  per 
square  inch  on  the  piston  during  the  forward  stroke,  then, 
since  the  work  done  is  equal  to  the  pressure  per  square 
foot  multiplied  by  the  volume  swept  through  in  cubic  feet, 
we  have 


(44) 


Fi  =  144  Pm  Fa. 


42  STEAM    ENGINES    AND    BOILERS 

From  (43)  and  (44)  we  get 


-f  hyp.  log.  ~ 

P       __v LL 

^m ~  F2 


v, 

The  ratio  ^  represents  the  number  of  times  the  steam  is 

Vl  V\ 

expanded.     If  this  ratio  be  denoted  by  r,  the  cut-off,  ~y  , 

will  be  —  ;  and  the  expression  for  the  mean  forward  pres- 
sure becomes 

1  +  llyp'  log'  r 


(46)  Pm    = 


On  the  return  stroke,  the  work,  W-2,  done  by  the  piston 
on  the  steam  is  that  represented  by  the  area  edfo,  and, 
from  the  figure, 

(47)  TF2  =  area  edfo  =  144  P3  F2. 

Since  the  effective  work,  W$t  done  by  the  steam  on 
the  piston  is  equal  to  that  done  on  the  forward  stroke 
minus  that  done  on  the  return  stroke,  we  have, 

(48)  TF3  =  TFi—  TF2  =  144  Pm  F2  —  144  P3  F2. 

If  we  let  PQ  be  the  mean  effective  pressure  per  square 
inch  on  the  piston,  we  shall  have 

(49)  TF3  =  144  Pe  F2  =  144  Pm  F2  —  144  P3  F2. 
Therefore,  from  (46)  and  (49), 


(50)      Pe  =  Pm_P3  = 


THEORY   OF   THE    STEAM    ENGINE.  43 

If  A  is  the  area  of  the  piston  in  square  inches,  and  L  is 
the  length  of  stroke  in  feet,  then 


Put  this  value  of  p2  in  (49)  and  we  get 

(52)  Ws  =  PeLA. 

Now  let  -A7"  be  the  number  of  forward  strokes  the  engine 
makes  per  minute.  For  a  double  acting  engine,  one  that 
takes  steam  on  both  sides  of  the  piston,  jVwill  be  equal 
to  twice  the  number  of  revolutions  made  by  the  engine 
per  minute  ;  and  for  a  single  acting  engine,  N  will  be  equal 
to  the  number  of  revolutions  made  per  minute.  Count- 
ing the  revolutions  made  by  an  engine  is  an  easy  method 
of  determining  the  value  of  N. 

The  work,  IV,  done  per  minute  by  the  engine  is,  evi- 
dently, N  W%,  and,  therefore,  from  (52), 

(53)  W=  PeL  AN. 

If  H.  P.  represents  the  horse  power  of  the  engine, 

C54)  HP=     -V-    -  Pe  LAN 

33UOO    "          3oOOU 

The  diagram  abcde,  in  Fig.  10,  is  termed  the  theoretical 
Indicator  Diagram  of  the  real  engine.  The  actual  dia- 
gram differs  from  that  in  Fig.  10  in  that,  owing  to  the 
friction  of  the  steam  in  the  ports  and  the  mechanical 
imperfections  in  the  valves,  the  corners  of  the  diagrams 
are  always  more  or  less  rounded.  The  line  ed  has  been 
drawn  as  if  the  back  pressure  were  constant,  while  as  a  mat- 
ter of  fact  it  is  not  ;  the  exhaust  usually  closes  before  all  of 
the  steam  has  been  forced  from  the  cylinder,  on  the 
return  stroke,  and  thus  confines  a  greater  or  less  quantity 


44  STEAM   ENGINES    AND    BOILERS. 

of  steam  in  the  cylinder  and  which  is  compressed  as  the 
piston  is  forced  back.  The  amount  of  this  compression 
may  be  great  or  small,  depending  upon  the  type  of 
engine,  but  the  greater  it  is  the  greater  is  made  the 
mean  back  pressure,  Ps.  The  absolute  value  of  P$  for 
engines  that  exhaust  into  the  atmosphere  will  vary  from 
16  to  20  Ibs.,  depending  upon  the  engine  ;  and  for  con- 
densing engines,  those  that  exhaust  into  a  condenser,  the 
absolute  value  of  Ps  will  vary  from  3^  to  8  Ibs.,  or  even 
higher.  The  dotted  lines,  in  Fig.  10,  show  how  the  theo- 
retical diagram  must  be  changed  to  conform  to  the  actual 
diagram. 

23.  CLEARANCE.  —  In  the  real  engine  the  piston  must 
not  touch  the  end  of  the  cylinder  when  at  the  end  of  the 
stroke,  and  there  is,  therefore,  a  space  of  greater  or  less 
volume  between  the  piston  and  the  cylinder  end.  In 
addition  to  this  volume  there  is,  also,  the  volume  of  the 
steam  ports  that  must  be  filled  by  steam.  The  sum  of 
these  two  volumes  form  what  is  termed  the  clearance, 
or  clearance  volume  of  the  engine. 

The  clearance  is  prejudicial  to  thermodynamic  effi- 
ciency of  the  real  engine,  as  it  preserves  a  volume 
of  what  might  be  termed  non-active  steam  subject  to 
condensation  ;  it  usually  increases  the  amount  of  steam 
required  to  do  a  given  amount  of  work,  and  decreases  the 
number  of  times  the  steam  is  expanded  for  a  given  cut-off. 

If  c  represents  the  volume  in  cubic  feet  of  the  clearance, 
the  volume  occupied  by  the  steam  at  the  point  of  cut- 
off will  be  V\  +  c;  and  at  the  end  of  the  stroke,  the 
volume  of  the  steam  will  be  Vi  +  c.  The  real  number  of 
times,  n,  the  steam  is  expanded  will  be 


T7" 
F2 


I/I 


THEORY    OF    THE    STEAM    ENGINE. 


45 


That   is,  the   clearance    has  reduced   the    number   of 
expansions,  r,  in  the  ratio  of 


If  we  call  m  the  ratio  of  the  clearance  volume,  cy  to  the 
volume,  J/2,  swept  through  by  the   piston  in  one    stroke, 

we  shall   have  m  =  • —    and,  from  (55), 


(55a) 


1  -f 


O      k 


Fig.  11, 


In  Fig.  II  let  a  b  c  d  e  represent  the  diagram  of  an 
engine  with  a  clearance  volume  c;  and  let,  as  before,  the 
expansion  line  b  c  be  an  equilateral  hyperbola. 

The  volume  occupied  by  the  steam  at  cut-off,  repre- 
sented by  the  line  h  b,  is  V\  -+•  c  =  a  b  -j-  h  a  ;  and  the 
pressure  per  square  inch  during  admission  is  the  initial 
pressure,  P\t  represented  by  the  line  b  g.  The  volume 
occupied  by  the  steam  at  the  end  of  the  stroke,  repre- 
sented by  the  line  i  d,  is  Vi-\-c  =  ed-}-ie;  and  the 


46 


STEAM    ENGINES    AND    BOILERS. 


THEORY    OF    THE    STEAM    ENGINE. 


47 


48  STEAM    ENGINES    AND    BOILERS. 

pressure  per  square  inch  against  which  the  piston  moves 
during  the  return  stroke  is  PS,  represented  by  the  line  df. 
The  work  done  during  the  forward  stroke  is  represented 
by  the  area  a  b  c  f  k.      By  inspection  we  see  that 


=  hbgo-\-bcfg  —  h  a  k  o. 
hbgo  =  144  PI  (  Fi  +  c). 

+  c 
bcfg=  144    I  Pd  V  =  144  P!  (Fi+c)  hyp.  log.  T/2 


/»ri  -i 
—  144    I  Pd  F  = 

JFo4-  n 


F2+c 

but    ^—       =  n,  from  (55),  and  hence 
v\-\-c 

b  cfg  ==  144  Pi  (Fi  +  c)  hyp.  log.  n. 
hako  =  144  PI  c. 

Therefore 
a  b  cf  k  =  144  Pl  (  V1  +  c)  (1  +  hyp.  log.  n)  —144  PI  c. 

If  we  let  P'm  represent  the  mean  forward  pressure  per 
square  inch,  the  work  done  during  the  forward  stroke  is 
144  P'm  V-2.  Putting  this  expression  equal  to  the  expres- 
sion for  a  b  c  f  k,  given  above,  we  have 

144  P'm  F2  =  144  P!  (  Fi  +  c)  (1  +  hyp.  log.  n)  —  PI  c. 
From  which  we  have 


l  (  1  +  hyp.  log.  „)  - 


But  -—  .  =  ;;z,  and  from  (55) 


14-  — 

F2_  1  +  m 


F2  w  F2 

Therefore 


(556)        P'm  =  Pi  (1  +  m)  ^^EJVK^vfi-y^  __  PI  m> 

n 


THEORY    OF    THE    STEAM    ENGINE.  49 

The  mean  effective  pressure  per  square  inch,  P'et  is  evi- 
dently the  mean  forward  pressure,  P'm,  less  the  back 
pressure,  P-A.  Hence 

(55c)     P'e=P'm  —  P3 


n 

This  expression  gives  the  true  mean  effective  pressure 
per  square  inch  when  clearance  is  taken  into  account. 
The  effect  of  clearance  is  not  only  to  reduce  the  number 
of  times  the  steam  is  expanded,  but  also  to  very  mate- 
rially change  the  expression  for  the  mean  effective  pres- 
sure, as  can  be  seen  by  comparing  (50)  and  (55^). 

24.  EFFICIENCY  OF  THE  ACTUAL  ENGINE. — The  thermo- 
dynamic  efficiency  of  the  actual  engine  is  expressed  by 
the  same  equation  as  the  efficiency  of  the  perfect  steam 
engine,  and  is 

*=J. 

Where  Wis  the  work  done  by  a  given  weight  of  steam, 
and  //is  the  total  heat  in  mechanical  units,  required  to 
raise  the  temperature  of  the  same  weight  of  water  from 
the  initial  temperature  of  the  water  up  to  the  temperature 
of  the  steam  and  there  turn  it  into  steam. 

The  work  done  per  stroke  by  an  engine  is,  from  (52), 
Pe  L  A,  and  the  volume,  in  cubic  feet,  of  the  steam,  at  the 

-IT 

initial  pressure,  used  per  stroke  is  V\=  — . 

L  A 

From  (51),  F2= ;  and,   therefore,    the    volume    of 

144 

steam  used  per  stroke  is 

LA 


(5G) 


144r 


If  s  is  the  volume  in  cubic  feet  of  one  pound  of  steam 
4 


50  STEAM    ENGINES    AND    BOILERS. 

at  the  initial  pressure,  as  given  in  Table  I,  the  weight,  S, 
of  steam  used  per  stroke  will  be 


Let  k\t  as  in  (29),  be  the  total  quantity  of  heat,  in  me- 
chanical units,  required  to  raise  the  temperature  of  one 
pound  of  water  from  the  initial  temperature  of  the  watef 
to  the  temperature  of  the  steam  and  there  convert  it  into 
steam.  Then  the  heat,  HI,  required  for  the  weight,  S,  of 
steam  used  per  stroke  will  be,  from  (57), 


(58) 


144  r  s 


Since  the  work  done  per  stroke  is  Pe  L  A,  and  the  heat 
used  per  stroke  is  //i,  the  efficiency  of  the  engine  is 


As  the  perfect  steam  engine  had  its  efficiency  de- 
creased by  departing  from  the  Carnot  cycle,  so  too,  the 
efficiency  of  the  actual  engine  is  less  than  that  of  the 
perfect  engine  the  more  it  departs  from  the  cycle  of  the 
perfect  engine.  In  the  perfect  engine  the  expansion  is 
always  continued  until  the  pressure  of  the  steam  is*that 
corresponding  to  the  temperature  of  the  feed  water.  In 
Fig.  7,  let  dm  be  the  pressure  of  the  steam  correspond- 
ing to  the  temperature  of  the  feed  water,  then  the  work 
done  by  the  perfect  steam  engine  would  be  represented 
by  the  area  abdcy  which  is  greater  than  the  work  that 
would  be  done  by  the  actual  engine,  by  the  area  d'de. 

The  actual  engine  loses  a  great  deal  of  heat  by  radia- 
tion and  conduction,  which  results  in  a  condensation  of 


THEORY   OF    THE    STEAM   ENGINE. 


51 


52  STEAM   ENGINES    AND    BOILERS. 

the  entering  steam ;  and  the  volume  of  steam  that  must 
be  applied  to  the  engine  is  Fi,  plus  that  required  for 
clearance,  plus  that  required  to  compensate  for  what  is 
condensed. 

A  part  of  the  work,  resulting  from  the  transformation 
of  the  heat  of  the  steam,  is  used  in  overcoming  the 
friction  of  the  moving  parts  of  the  actual  engine ;  so 
that  the  engine  has  a  mechanical  efficiency  as  well  as  a 
thermodynamic  efficiency,  and  the  two  must  be  care- 
fully distinguished  from  one  another 


CHAPTER     III. 

TYPES    AND    DETAILS    OF    ENGINES. 

25.  CLASSIFICATION  OF  ENGINES.  —  Engine  builders 
usually  classify  their  engines  in  two  great  classes  as 
follows :  — 

1.  Condensing  Engines. 

2.  Non-condensing  Engines. 

Condensing  engines  are  those  that  exhaust  the  steam 
into  a  condenser;  they  may  be  either  simple,  have  but  a 
single  cylinder,  or  compound,  have  two  or  more  cylinders. 
While  a  condensing  engine  maybe  a  simple  engine, most 
of  them  are  compound  and  expand  the  steam  a  greater 
number  of  times  than  could  be  well  done  in  a  simple 
engine.  The  mean  back  pressure,  P3  in  Art.  22,  is 
always  less  than  atmospheric  pressure  in  the  case  of  a 
condensing  engine. 

Non-condensing  engines  are  those  that  exhaust  the 
steam  into  the  atmosphere  ;  and,  while  they  may  be  either 
simple  or  compound,  they  are  usually  simple.  The  mean 
back  pressure  in  these  engines  is  always  greater  than  the 
atmospheric  pressure,  when  the  engine  is  running 
properly. 

Engines  are  sometimes  classified  according  to  whether 
they  are  used  on  land  or  on  the  ocean,  as  Land  engines 
and  Marine  engines. 

They  may  be  classified  according  to  the  position  of  the 
cylinder,  as  Vertical  engines  or  Horizontal  engines. 

(53) 


54 


STEAM    EXGINES    AND    BOILERS. 


In  this  work,  all  engines  will  be  considered  as  coming 
under  one  of  the  following  heads  :  — 

1.  Plain  Slide  Valve  Engines. 

2.  Automatic  High  Speed  Engines. 

3.  Corliss  Engines. 

There  are   engines   on  the  market  that  on  account  of 
peculiarities  of  design  it  would  be  extremely  difficult  to 


Fig.  15.  Horizontal  Section. 
Cylinder,  Dick  and  Church  Engine, 

determine  exactly  under  which  head  they  would  belong; 
but  such  engines  must  be  considered  simply  as  connect- 
ing links,  in  which  an  endeavor  has  been  made  to  obtain 
all  the  good  qualities  of  the  engines  of  two  or  more 
types.  Such  engines  are  often,  however,  unfitted  for  any 
special  kind  of  work,  as  they  possess  to  a  certain  degree 
qualities  that  make  them  better  than  is  necessary  for 
some  work,  and  yet  do  not  possess  the  same  qualities  to 


TYPES    AND    DETAILS    OF    ENGINES.  55 

a  sufficiently  high  degree  to  make  them  well  fitted  to  do 
other  special  work. 

26.  PLAIN  SLIDE  VALVE  ENGINES.  —  These  engines  are 
usually  plain  in  appearance,  and  use  a  simple  form  of  D- 
valve.  Some  are  heavy,  well  made,  and  made  of  good 
material;  others  are  slight  in  weight,  poorly  made,  and' 
made  of  the  poorest  material.  To  this  type  of  engines 
belong  most,  if  not  all,  of  the  very  cheap  engines. 
Engines  of  this  type,  however,  will  stand  more  hard  usage 
and  neglect  than  perhaps  any  other  on  the  market;  good 
ones,  of  course,  will  stand  more  than  cheap,  poor  ones. 
They  have  rather  gone  out  of  fashion  at  present,  and  yet, 
for  some  conditions  and  some  kinds  of  work,  they  are 
good  engines. 

Engines  of  this  type  have  a  fixed  cut-off,  which  can 
only  be  changed  by  re-adjusting  the  engine,  and  they 
regulate  by  throttling  the  incoming  steam  so  as  to  reduce 
the  initial  pressure  in  the  cylinder.  The  cut-off  usually 
occurs  at  about  three-fourth  stroke ;  the  clearance  is  about 
ten  to  twelve  per  cent  of  the  volume  swept  through  by  the 
piston ;  and  there  is  little  compression  of  Che  exhaust  steam. 
It  results,  therefore,  that  as  the  steam  has  practically  no 
expansion,  these  engines  are  not  economical  in  the  use  of 
steam. 

The  mean  back  pressure  for  engines  of  this  type  may 
be  taken  as  about  seventeen  or  eighteen  pounds  absolute. 

In  favor  of  engines  of  this  type  it  may  be  said  that  they 
are  simple  in  construction  ;  require  very  little  attention ; 
are  difficult  to  put  much  out  of  order,  and  are  easily 
repaired  when  deranged.  They  are  suitable  for  out-of- 
the-way  places  where  facilities  for  repairs  are  few,  and 
for  places  where  fuel  is  cheap  and  the  work  to  be  done  is 
practically  constant. 

The  mechanical  efficiency,  as  well  as  the  thermody- 
namic  efficiency,  of  engines  of  this  type  is  often  small. 


OO  STEAM    ENGINES    AND    BOILERS. 

In  Fig.  8  is  shown  a  section  of  an  engine  of  this  type, 
and  in  Fig.  9  is  shown  a  side  view  of  one. 

27.  AUTOMATIC  HIGH  SPEED  ENGINES. —  This  type  of 
engines  may  be  considered  as  the  modern  type,  as  it  has 
been  evolved  since  the  beginning  of  the  great  use  of 
electricity,  and,  indeed,  is  the  result  of  the  demand  for  an 
engine  to  be  used  to  run  electric  machinery.  With  the 


Fig.  16.  Cross-section. 
Cylinder,  Dick  and  Church  Engine. 

advent  and  great  use  of  dynamos  there  was  at  once  a 
demand  for  small  engines  that  could  run  at  a  high  rota- 
tive speed,  that  would  be  fairly  economical  under  fluctu- 
ating loads,  and,  above  all,  would  run  at  a  uniform  speed 
under  great  changes  of  load.  The  plain  slide-valve  type 
of  engines  could  not  be  said  to  satisfy  any  one  of  these 
conditions;  the  Corliss  engine  did  not  satisfy  the  first 


TYPES    AND    DETAILS    OF    ENGINES.  57 

condition  as  to  high  rotative  speed,  and,  then,  they  were 
too  large,  and,  for  small  plants,  occupied  too  much  space. 
Engines  of  this  type  are  termed  high  speed  not  on 
account  of  the  speed  of  the  piston,  but  on  account  of 
the  number  of  revolutions  they  will  make  per  min- 
ute. The  speed  of  the  engine  is  kept  almost  con- 
stant by  automatically  changing  the  point  of  cut-off  and 
the  amount  of  compression  to  suit  the  various  fluctuations 
of  the  load.  The  increase  or  diminution  in  the  number 
of  revolutions  will  usually  be  about  one  per  cent,  or  less, 
for  a  sudden  change  of  from  full  load  to  no  load,  or  no 
load  to  full  load.  This  increase  or  diminution  of  speed, 
however,  will  seldom  last  more  than  a  few  revolutions. 
The  number  of  revolutions  made  by  an  engine  of  the 
automatic  high  speed  type  will  depend  upon  the  length 
of  stroke  and  upon  the  make ;  the  shorter  the  stroke 
the  greater  the  number  of  revolutions.  Ordinarily,  the 
number  of  revolutions  that  an  engine  of  this  type  will 

make  may  be  obtained  by  the  formula,  N=  ~ 

v  Ll 

Where  N  is  the  number  of  revolutions  made  per  min- 
ute ;  and  L,  the  length  of  the  stroke  in  inches. 

On  account  of  the  high  speed  of  rotation,  engines  of 
this  type  must  have  large,  ample  bearings ;  all  parts  must 
be  carefully  proportioned,  fitted  and  adjusted,  and  made 
of  good  material.  The  greatest  source  of  trouble  with 
these  engines,  which  is  overheating  of  bearings,  can 
usually  be  traced  to  poor  materials  and  workmanship. 

Engines  of  this  type  almost  invariably  use  some  form 
of  balanced  valve,  which  is  automatically  made  to  change 
the  amount  of  steam  admitted  to  the  cylinder  in  such  a 
manner  that  the  amount  of  steam  admitted  is  nearly 
proportional  to  the  work  to  be  done  by  the  engine. 

The  cylinders  of  engines  of  this  type  are  usually  of 
comparatively  large  diameter  and  short  stroke  ;  the 
diameter  is  usually  between  0.60  and  0.80  of  the 


58 


STEAM    ENGINES    AXD    BOILERS. 


stroke,  and  is  often  equal  to  the  length  of  the  stroke. 
These  proportions  of  cylinders  mean  a  short  engine  for  a 
given  horse  power,  and  a  comparatively  large  clearance. 
The  clearance  varies  from  about  5  to  10  per  cent  of  the 
volume  swept  through  by  the  piston ;  it  may  usually  be 


o> 

"I 

t£    3 


taken  as  about  IO  per  cent  for  those  engines  having  a 
single  valve,  and  4  to  6  per  cent  for  those  having  a  system 
of  multiple  valves. 

The  mean   back  pressure  for  engines  of  this  type  may 
be  taken  as  about  eighteen  or  twenty  pounds  absolute. 


TYPES    AND    DETAILS    OF    ENGINES.  59 

Most  engines  of  this  type  have  a  center  crank,  although 
some  are  made  with  a  side  crank. 

Summing  up,  it  may  be  said  in  favor  of  engines  of  this 
type  that  they  are  fairly  economical  in  the  use  of  steam ; 
occupy  small  space  for  a  given  power  ;  regulate  well 
under  a  fluctuating  load ;  and,  as  compared  to  engines  of 
the  Corliss  type,  are  of  small  first  cost. 

The  engines  of  this  type  require  careful  attention  to  be 
paid  to  the  bearings,  on  account  of  the  high  speed  of 
rotation,  and  to  the  adjustments  of  the  valves  and  other 
moving  parts.  All  bearings  must  be  kept  in  good  con- 
dition and  well  lubricated. 

Figs.  II  and  12  illustrate  engines  of  this  type. 

28.  CORLISS  ENGINES. —  Under  this  head  the  author 
includes,  in  addition  to  the  engines  of  the  pure  Corliss  type, 
all  of  those  engines  that,  even  though  not  having  the  Cor- 
liss valve  gear,  have  more  of  the  characteristics  of  the 
Corliss  engines  than  of  the  engines  of  the  types  already 
described.  Engines  of  this  type,  while  having  a  high 
velocity  of  piston,  have  a  rather  slow  speed  of  rotation; 
even  the  smaller  sizes  seldom  make  more  than  100  revo- 
lutions per  minute.  This  is  due  principally  to  the  nature 
of  the  valve  gearing  used  to  operate  the  valves.  An  aver- 
age value  of  the  number  of  revolutions  made  per  minute 
by  engines  of  this  type  will  be  given  by  the  equation 

N=   y  -—,  where  L  is  the  length  of  stroke  in  inches. 

V  J^i 

The  cylinders  of  engines  of  this  type  are  usually  of 
comparatively  small  diameter  and  long  stroke.  The  dia- 
meter varies  from  one-third  to  two-thirds  the  length  of  the 
stroke,  but  is  usually  about  one-half  the  length  of  the 
stroke.  These  proportions  of  cylinders  mean  a  long 
engine,  occupying  much  space,  for  a  given  horse-power. 

Engines  of  this  type  usually  use  a  system  of  multiple 
valves,  which,  by  means  of  suitable  mechanism,  are  made 


60 


STEAM    ENGINES    AND    BOILERS. 


to  cut-off  the  steam  to  suit  the  requirements  of  the  load, 
without  changing  the  amount  of  compression  of  the  ex- 
haust steam.  There  is  usually  one  steam  valve  and  one 
exhaust  valve  for  each  end  of  the  cylinder,  and  the  gov- 
erning mechanism  changes  the  action  of  the  steam  valve 
only. 

In  order  to  preserve  a  uniform  velocity  of  rotation,  the 
engines  of  this  type  not  only  have  the  cut-off  automati- 


Fig.  18. 
Cylinder,  Porter-Allen  Engine. 

cally  changed  to  suit  the  varying  fluctuations  of  the  load, 
but  are  provided,  also,  with  large  heavy  fly-wheels,  in 
which  surplus  energy  is  stored  when  the  load  is  de- 
creased, and  from  which  energy  may  be  drawn  when 
the  load  is  suddenly  increased.  By  the  aid  of  the  au- 
tomatic cut-off  valves  and  the  large  fly-wheels,  the  varia- 
tion in  speed  of  engines  of  this  type  may  be  made  as 
small  as  desired. 


TYPES    AND    DETAILS    OF    ENGINES.  61 

The  clearance  in  engines  of  this  type  is  usually  about 
2  per  cent  of  the  volume  swept  through  by  the  piston, 
although  it  varies  from  I  to  4  or  5  per  cent  of  that 
volume. 

The  mean  back  pressure  for  engines  of  this  type  may 
be  taken  as  about  16  to  18  pounds  absolute. 

As  the  engines  of  this  type  make  comparatively  few 
revolutions  per  minute,  the  bearings  are  not  so  apt  to  get 
hot  as  in  the  case  of  engines  of  the  automatic  high 
speed  type. 

This  type  of  engines  is  the  most  economical  of  all 
types,  and  for  large  establishments  requiring  much  power 
is  undoubtedly  the  best.  The  engines  of  this  type,  how- 
ever, are  of  greater  first  cost,  and  occupy  more  space 
than  do  engines  of  the  automatic  high  speed  type. 
They  require  considerable  care  and  attention,  and  have  a 
number  of  small,  light  parts  to  be  kept  in  repair  and 
adjustment. 

Engines  of  this  type  are  illustrated  by  Figs.  13  and  14. 

29.  CYLINDER  AND  VALVE  CHEST. —  The  cylinders  of 
engines  are  made  of  cast  iron,  with  walls  sufficiently 
thick  to  stand  the  stress  induced  by  the  pressure  of  the 
steam,  and,  also,  the  straining  due  to  the  motion  of  the 
piston  back  and  forth.  The  thickness  should  be  such  as 
to  allow  at  least  one  reboring.  They  are  all  true  cylinders 
inside,  but  the  shape  of  the  outside  will  'depend  upon  the 
style  of  engine  and  the  maker.  Most  cylinders  for  short 
stroke  engines  overhang  the  beds  of  the  engines  ;  some  are 
cast  solid  with  the  beds,  others  are  cast  separate  and 
bolted  on.  This  last  form  is  perhaps  the  better,  as  the 
cylinder  can  then  be  rebored  with  less  trouble. 

The  steam  chest  is  usually  cast  with  the  cylinder, 
although  it  is  sometimes  cast  separate  and  bolted  on.  Its 
form  and  dimensions  depend  upon  the  valve,  ports,  and 
type  of  the  engine. 


STEAM   ENGINES   AND   BOILERS. 


o 
ti 


TYPES    AND    DETAILS    OF    ENGINES.  63 

The  ports  should  be  large,  with  smooth  surfaces  and 
without  any  sharp  or  abrupt  changes  in  direction.  The 
area  of  cross-section  of  the  ports  should  be  such  that  the 
steam  will  travel  at  a  velocity  between  100  and  1 50  feet  per 
second  when  passing  into  the  cylinder.  The  ports  should 
slope  from  the  cylinder  towards  the  steam  chest,  so  that 
all  water  that  is  condensed  in  the  cylinder  may  easily 
drain  away. 


Fig.  20. 
Cylinder  of  Corliss  Engine. 

All  cylinders  should  be  provided  with  drip  cocks,  for 
draining  the  cylinder  and  steam  chest. 

Some  of  the  various  methods  of  inserting  the  heads, 
and  protecting  the  cylinders  by  lagging,  are  shown  in  the 
cuts  of  cylinders  in  this  work. 


64  STEAM    ENGINES    AND    BOILERS. 

30.  PISTON. —  The  main  point  to  be  considered  in  con- 
nection with  a  piston  is  tightness,  as  a  leaky  piston 
reduces  the  efficiency  of  the  engine  very  materially.  For 
engines  of  the  high  speed  automatic  type,  where  the 
weight  of  the  reciprocating  parts  is  used  to  aid  in  regu- 
lating the  engine,  weight  is  of  an  advantage  rather  than  a 
disadvantage  ;  while  in  the  case  of  engines  of  the  Corliss 
type,  weight  is  a  disadvantage.  The  pistons  of  engines 
of  the  automatic  high  speed  type  are,  usually,  much 
thicker  in  proportion  to  the  diameter,  than  those  of  the 
Corliss  type. 

Pistons  are  usually  made  tight  by  using  as  "packing 
rings,"  split  cast  iron  rings  that  are  turned  slightly  larger 
in  diameter  than  the  bore  of  the  cylinder.  When  they 
are  in  the  cylinder,  the  elasticity  of  the  cast  iron  keeps 
the  rings  pressed  out  against  the  cylinder,  and  thus  pre- 
vents the  passage  of  the  steam.  The  piston  may  be  a 
single  casting,  with  grooves  into  which  the  packing  rings 
are  sprung,  or  may  be  built  up,  as  shown  in  Fig.  2 1 .  There, 
A  is  the  "spider;"  C,  the  "chunk"  or  "bull  "ring;  D, 
the  "packing  ring;"  and  E,  the  "follower  plate." 
The  bolts  marked  O  are  for  adjusting  the  bull  ring  so 
that  it  will  always  run  true  in  the  cylinder,  even  if  the 
center  of  the  piston  rod  should  not  coincide  with  the 
center  of  the  cylinder. 

31.  CROSS-HEAD. —  The  cross-head  consists  of  the  body 
of  the  cross-head,  the  "  slippers  "  or  bearing  surfaces,  and 
the  "  cross-head  pin." 

The  cross-head  is  guided  in  its  backward  and  forward 
motion  by  the  bearing  surfaces  of  the  top  and  bottom 
"guides."  Center  crank  engines  have  usually  two  top 
guides  and  two  bottom  guides,  as  the  cross-heads  are 
made  with  two  sets  of  bearing  surfaces,  one  at  each  end 
of  the  cross-head  pin,  as  shown  in  Fig.  22 ;  while  side 
crank  engines  have  usually  one  top  guide  and  one  bot- 
tom guide,  as  the  cross-heads  have  the  general  form 
shown  in  Fig.  23.  For  automatic  high  speed  engines,  the 


TYPES    AND    DETAILS    OF    ENGINES. 


65 


bearing  surfaces  are  usually  plane  surfaces,  as  shown  in 
Fig.  22 ;  while  for  Corliss  engines,  they  are  usually  V- 
shaped,  or  cylindrical  as  shown  in  Fig.  23.  Engines  are 
usually  run  "over,"  so  as  to  bring  the  pressure  of  the 
cross-heads  always  on  the  bottom  gudes  :  that  is,  the  en- 
gines are  run  so  that  an  observer  facing  an  engine  with 
his  left  hand  towards  the  cylinder,  sees  the  fly-wheel  re- 
volve from  left  to  right.  The  bearing  surfaces  of  the 
cross-heads  are  usually  made  of  some  anti-friction  wear- 
ing metal,  such  as  Babbitt  metal,  and  care  should  be 


Fig.  21. 

taken  to  keep  them  well  lubricated.  It  is  always  best 
to  have  some  arrangement  by  means  of  which  adjust- 
ment may  be  made  for  the  wear  of  the  slippers,  so  as  to 
keep  the  line  of  motion  of  the  center  of  the  cross-head 
pin  coincident  with  the  center  line  of  the  cylinder.  If 
there  is  no  means  of  adjusting  for  the  wear,  and  the  line 
of  motion  of  the  center  of  the  cross-head  pin  is  not  coin- 
cident with  the  center  line  of  the  cylinder,  the  friction  on 
the  cross- head  pin  and  crank  pin  is  increased,  and,  also, 
the  cross-head  will  run  loose  in  the  guides  and  cause  a 
knocking  noise  when  the  load  on  the  engine  is  suddenly 
changed. 

The  cross-head  pin  is  sometimes  cast   solid  with  the 
body  of  the  cross-head,  and  then  turned  up  either  by  hand 


66 


STEAM    ENGINES    AND    BOILERS. 


or,  if  the  shape  of  the  cross-head  permits,  by  machinery ; 
often,  however,  the  pin  is  made  separate  and  put  into  the 
cross-head.  This  last  method  gives  no  advantage,  to  the 
user  of  the  engine,  over  the  method  of  making  the  pin  and 
cross-head  body  one  casting,  unless  the  pin  is  put  into 
the  body  in  such  a  way  that  it  can  be  removed  at  any 
time  for  returning.  Separate  pins  are  usually  made  of 
steel.  Many  engine  builders  flatten  the  top  and  bottom 
of  the  cross-head  pin  in  order  to  reduce  the  wear.  It  is 


Fig.  22. 
Cross-head,  Porter-Allen  Engine. 


doubtful,  however,  whether  this  practice  attains  its  ob- 
ject.    Ample  facilities   should  be  provided  for  good  and 
proper  lubrication  of  the  cross-head  pin. 
Cross-heads  are  shown  in  Figs.  22  and  23. 


TYPES   AND   DETAILS    OF   ENGINES, 


67 


Fig.  23. 
Cross-head,  Ide  Engine. 


68  STEAM    ENGINES    AND    BOILERS. 

32.  CONNECTING  ROD. —  The  motion  of  the  cross-head 
is  transmitted  to  the  crank-pin  through  the  connecting 
rod,  which  is  always  made  either  of  wrought  iron  or  steel. 
If  it  is  assumed  that  the  crank-pin  moves  with  a  uniform 
velocity,  the  length  of  the  connecting  rod  will  have  a 
marked  influence  upon  the  velocity  of  the  cross-head. 
If  the  connecting  rod  could  be  so  arranged  that  it  would 
always  remain  parallel  to  the  line  of  motion  of  the  piston, 
then  the  distance  that  the  piston  has  moved  from  the  end 
of  its  stroke,  for  a  given  movement  of  the  crank,  would 
always  be  equal  to  the  distance  from  the  position  of  the 


Fig.  24. 

crank-pin  when  on  dead  center  to  the  foot  of  a  perpen- 
dicular let  fall  from  the  crank-pin  on  the  line  of  motion 
of  the  piston. 

In  Fig.  24,  let  B  represent  the  cross-head  of  an  engine, 
which  being  rigidly  connected  to  the  piston  has  the  same 
motion  as  the  piston ;  and  let  the  line  BC  represent  the  line 
of  motion  of  the  piston.  Also,  let  A  represent  the  center 
of  the  crank-pin  revolving  about  C  and  connected  to  B 
by  the  connecting  rod  BA.  Now,  if  the  rod  were  infinitely 
long  it  would  always  remain  parallel  to  the  line  BCt  and 
the  distance  that  the  piston  would  have  moved  while  the 
crank  moved  from  a\  to  A  would  be  equal  to  the  distance 
a\  d.  Since,  however,  the  connecting  rod,  BA,  does  not 
remain  parallel  to  BC,  but  is  oblique  to  it,  for  all  positions 


TYPES    AND    DETAILS    OF    ENGINES. 


69 


of  the  crank -pin  except  at  a\  and  #2,  the  distance,  b\  B, 
that  the  piston  actually  is  from  the  end  of  its  stroke  is 
not  equal  to  a\  d.  As  will  be  shown 
in  Art.  47,  it  is  known  that  during 
the  forward  stroke  the  distance  the 
piston  moves  from  the  end  of  the 
stroke,  for  a  given  motion  of  the 
crank-pin,  is  greater  than  it  would 
be  if  there  were  no  obliquity  to  the 
connecting  rod  ;  and  during  the  re- 
turn stroke,  the  movement  of  the 
piston  is  less  than  it  would  be  if  there 
were  no  obliquity. 

The  length  of  the  connecting  rod 
is  usually  made  equal  to  three  times 
the  length  of  the  stroke  for  Corliss 
engines,  and  about  two  and  a  half 
times  the  length  of  the  stroke  for 
automatic  high  speed  engines. 

The  cross-section  of  the  connect- 
ing rod  of  a  Corliss  engine  is  usually 
a  circle,  and  that  of  the  connecting 
rod  of  an  automatic  high  speed  en- 
gine is  usually  a  rectangle  whose 
greatest  dimension  is  the  depth  of 
the  rod. 

The  connecting  rod  has  at  one  end 
the  "  cross-head  pin  brasses,"  and  at 
the  other,  the  "  crank-pin  brasses." 
The  "brasses  "  are  castings  of  brass, 
fastened  to  the  connecting  rod  in 
various  ways,  which  form  the  bearing 
surfaces  of  the  rod  on  either  the 
cross-head  pin  or  the  crank-pin.  In 

order  that,  as  the   brasses  wear,  the   length  of  the   rod, 
measured  from  center  of  cross-head  brasses  to  center  of 


70 


STEAM    ENGINES    AND    BOILERS. 


crank-pin  brasses,  may  remain  constant,  it  is  necessary  to 
provide  a  means  of  taking  up  the  wear. 

In  Fig.  25  is  shown  a  connecting  rod  whose  cross-head 


Fig.  26. 
Connecting  Rod,  Porter-Hamilton  Eogine. 

end  is  of  a  solid  box  form,  into  which  the  brasses  fit;  the 
crank -pin  end  has  the  brasses  attached  to  it  by  means  of 
a  "  strap/'  held  by  a  gib  and  key.  The  method  of  taking 
up  the  wear  of  the  brasses  is  indicated  in  the  cut. 


Fig.  27. 
Connecting  Rod,  Woodbury  Engine. 

In  Fig.  26  is  shown  a  connecting  rod  whose  crank  end 
is  of  the  "  marine "  type,  sometimes  known  as  "  club 
ended; "  the  cross-head  end  has  the  strap  attached  to  the 
rod  by  a  bolt,  and  a  gib  and  key. 


TYPES    AND    DETAILS    OF    ENGINES, 


71 


72 


STEAM    ENGINES    AND    BOILERS. 


Fig.  27  shows  a  connecting  rod  whose  cross-section  is 
I-shaped.  The  method  of  attaching  the  brasses  and 
taking  up  the  wear  is  clearly  shown. 

33.  CRANK. —  Those  engines  that  have  the  crank 
between  the  two  main  bearings  of  the  shaft  are  center- 
crank  engines ;  and  those  that  have  the  crank  on  the  same 
side  of  both  the  shaft  bearings  are  side-crank  engines. 


Fig.  29. 


Most  center-crank  engines  are  of  the  automatic  high 
speed  type,  and  have  the  crank  and  the  shaft  forged  out  of 
one  solid  piece  of  iron  or  steel.  Where  this  is  the  case  it 
is,  usually,  customary  to  fasten  to  each  arm  of  the 
crank  a  cast  iron  disk  provided  with  a  balance  weight 
to  balance  the  weight  of  the  crank  and  a  part  of  the 
weight  of  the  connecting  rod.  The  method  of  fastening 
these  balancing  disks  to  the  crank  differs  for  different 
makes  of  engines.  Some  center-crank  engines  have  a 


TYPES    AND    DETAILS    OF    ENGINES. 


73 


built  up  crank ;  the  shaft  is  made  of  two  pieces,  to  the 
end  of  each  of  which  is  fastened  a  disk  or  wheel,  and 
these  disks  are  then  fastened  together  by  the  crank  pin. 
The  disks  are,  usually,  forced  on  the  pieces  of  the  shaft 
by  hydraulic  pressure,  and  then  keyed.  The  pin  is,  also, 
forced  into  the  disks  by  hydraulic  pressure. 

The  diameter  of  the  crank-pin  of  center-crank  engines 
is   almost   invariably    the  same  as,    of   slightly    greater 


Fig.  30. 


than,  the  diameter  of  the  shaft ;  and  it's  length  is  usually 
equal  to  that  of  the  cross-head  pin. 

In  Figs.  28  and  29  are  shown  the  forms  of  center- 
cranks  that  have  been  described.  Fig.  28  shows  the 
crank  of  the  Woodbury  engine,  and  Fig.  29  shows  the 
built  up  center-crank  of  the  Straight  Line  engine. 

Side  crank  engines  may  have  simply  a  crank,  forced  by 
hydraulic  pressure  onto  the  end  of  the  shaft,  into  which 


74  STEAM    ENGINES    AND    BOILERS. 

the  crank-pin  is  forced;  or  they  may  have  a  disk,  termed 
the  crank-disk,  forced  onto  the  end  of  the  shaft,  which 
carries. the  crank-pin. 

Most  engines  of  the  Corliss  type  have  simply  a  crank, 
while  the  side-crank  engines  of  the  automatic  high  speed 
type,  usually,  have  a  crank-disk. 

The  crank-pin  of  side-crank  engines  is,  usually,  about 
the  same  size  as  the  cross-head  pin.  The  method  of 
fastening  the  crank-pin  into  the  crank,  or  the  crank-disk, 
varies  with  different  makes  of  engines.  Some  are  simply 
forced  into  the  hole,  provided  for  them,  by  hydraulic 
pressure;  others  are  forced  in,  and  then  have  a  nut 
put  on  the  back  ;  while  others  are  fastened  in  by  other 
methods. 

It  is  of  the  utmost  importance  that  ample  provisions  be 
made  for  the  proper  lubrication  of  the  crank-pin  of  all 
engines,  whether  side-crank  or  center-crank. 

34.  MAIN  BEARINGS. —  It  is  important  that  the  main 
bearings  of  an  engine  be  large,  lined  with  a  good 
wearing  metal,  and  have  proper  facilities  for  lubricating. 
Small  bearings,  or  those  not  having  proper  provisions  for 
distributing  the  oil  over  the  bearings,  are  apt  to  give 
trouble  by  running  too'  hot  and  being  constantly  in 
danger  of  cutting. 

The  caps  to  the  main-bearings  are  those  pieces  that  go 
down  over  the  shaft  after  it  is  in  the  bearings.  They  are 
sometimes  put  on  in  a  horizontal  position  and  other  times 
are  inclined  at  an  angle  of  about  30°. 

In  Fig.  30  is  shown  a  section  of  the  main  bearing  of 
the  Porter-Allen  Automatic  Engine.  It  is  made  in  four 
parts,  viz.,  the  bed,  or  bottom  part;  the  side  boxes,  or 
side  parts  ;  and  the  cap,  or  top  part  of  the  bearing.  By 
screwing  up  the  nuts  marked  a,  the  wedges  may  be 
raised,  and  the  side  boxes  pressed  out  and  tightened 
against  the  shaft. 


TYPES    AND    DETAILS    OF    ENGINES. 


75 


In  Fig.  31  is  shown  a  section  of  the  main  bearing  of 
the  Porter-Hamilton  Engine. 

35.  ECCENTRIC. —  The  eccentric  is  simply  a  cast  iron 
disk  through  which  the  shaft  passes  and  which  moves  the 
valve  of  the  engine.  In  the  case  of  engines  of  the  plain 
slide  valve  type,  and,  also,  of  the  Corliss  type,  the 
eccentric  is  fastened  to  the  shaft  either  by  a  key  or  by  a 
set  screw.  The  advantage  of  the  set  screw  over  the  key 


Fig.   31 


is  that  it  allows  the  relative  position  of  the  eccentric  on 
the  shaft  to  be  changed  at  will ;  and  the  disadvantage  is 
that  at  times  the  eccentric  may  slip  and  change  its 
relative  position  without  that  fact  being  known. 

The  distance  that  the  center  of  the  eccentric  is  from 
the  center  of  the  shaft  is  its  eccentricity.  The  eccentric 
is  equivalent  to  a  crank  whose  length  is  equal  to  the 
eccentricity,  and  takes  the  place  of  such  a  crank.  As  the 
shaft  is  turned,  the  eccentric  turns  and  moves  the  valve  of 
the  engine  back  and  forth  as  if  it  were  connected  to  a 
crank  whose  length  is  equal  to  the  eccentricty  of  the 
eccentric. 


76 


STEAM    ENGINES    AND    BOILERS. 


On  most  engines  of  the  automatic  high  speed  type,  the 
eccentric  is  not  fastened  to  the  shaft,  but  the  opening 
through  which  the  shaft  passes  is  larger  than  the  shaft ; 
so  that  the  relative  position  of  the  eccentric  and,  also,  the 
eccentricity  can  be  automatically  changed  by  the  gov- 


Fig.  32. 

erning  device.  Changing  the  eccentricity,  of  course, 
changes  the  travel  of  the  valve,  and,  as  we  shall  see  later, 
this  affects  the  point  of  cut-off. 

36.  GOVERNORS. —  It  is  impossible  to  discuss  here  the 
governing  device  of  either  the  automatic  high  speed  type 


TYPES    AND    DETAILS    OF    ENGINES.  77 

of  engines  or  the  Corliss  type,  as  that  involves  the  dis- 
cussion of  the  valve  mechanisms  that  will  be  given  later. 
The  governor  used  on  engines  of  the  plain  slide  valve 
type  is  a  "  throttling  governor,"  which  is  attached  to  the 
steam  pipe  and  which  decreases  the  pressure  of  the  enter- 
ing steam  by  "  throttling,"  or  partially  closing  an  admis- 
sion valve.  In  Fig.  32  is  shown  a  section  of  one  of  these 
governors.  The  opening  A  is  connected  to  the  steam 
chest,  and  the  opening  B  to  the  steam  pipe,  so  that  the 
steam  passes  through  the  valve  C  before  entering  the 
engine.  The  gear  wheel  D  is  run  by  means  of  a  belt, 
from  the  shaft  of  the  engine  to  the  wheel  E,  and  it,  in 
turn,  runs  the  gear  wheel  Fy  which  moves  the  balls  G. 
As  the  speed  of  the  balls  G  increases,  the  centrifugal 
force  makes  them  rise,  and  in  doing  so  they  force  down 
the  valve-stem  Ht  and  partly  close  the  valve  C.  The 
faster  the  engine  runs,  the  faster  the  balls  G  move,  and 
the  more  the  valve  C  is  closed ;  the  slower  the  engine 
goes,  the  slower  the  balls  move,  and  the  more  the  valve  C 
is  opened.  The  valve  C,  thus  automatically  opens  wider  to 
admit  steam  if  the  engine  begins  to  slow  down,  and  partly 
closes,  thus  shutting  off  the  steam,  if  the  engine  begins 
to  speed  up.  By  properly  adjusting  the  governor,  by 
means  of  the  screw  7",  the  speed  of  the  engine  may  be 
fairly  controlled  within  certain  limits. 


CHAPTER     IV. 

ADMISSION    OF    STEAM    BY    VALVES. 

37.  OPENING  AND  CLOSINGTHE  PORTS  BY  THE  VALVE. — 
As  has  been  explained,  the  valve  is  worked  by  an  eccen- 
tric which  is  fastened  to  the  shaft;  and  the  eccentric  is 
equivalent  to  a  crank  whose  length  is  equal  to  the 
eccentricity  of  the  eccentric.  The  motions  of  the 
eccentric  and  the  valve,  therefore,  bear  the  same  relations 
to  one  another  that  the  motions  of  the  crank  and  piston 
do.  During  one  complete  revolution  of  the  shaft  the 
valve  makes  one  complete  forward  and  one  complete 
backward  motion,  and  the  length  of  each  of  these 
motions  is  equal  to  twice  the  eccentricity  of  the  eccentric. 
If  we  neglect  the  obliquity  of  the  eccentric  rod,  which 
changes  the  motion  of  the  valve  in  the  same  way  that  the 
obliquity  of  the  connecting  rod  changes  the  motion  of 
the  piston,  the  valve  will  make  one-half  of  its  forward,  or 
backward,  motion  while  the  eccentric  makes  a  quarter  of 
a  revolution,  and  the  relation  of  the  motion  of  the  valve 
to  that  of  the  eccentric  will  be  very  much  simplified. 
In  all  that  follows,  except  when  otherwise  stated,  the 
obliquity  of  the  connecting  rod,  and  of  the  eccentric  rod, 
will  be  neglected  ;  and  the  motions  of  the  valve  and  the 
piston  will  be  discussed  as  if  the  rods  were  of  infinite 
length. 

The  valve  is  said  to  be  in  "  mid-position  "  when  it  has 
reached  the  middle  of  its  forward  or  backward  motion. 

The  "  travel"  of  the  valve  is  the  total  distance  that  it 
moves  in  one  direction,  either  forward  or  backward,  and 
is  equal  to  twice  the  eccentricity  of  the  eccentric. 
(78) 


ADMISSION    OF    STEAM    BY    VALVES.  79 

The  simplest  valve  is  the  plain  Z?-valve,  shown  in  Fig. 
33.  There,  a  represents  the  steam  chest,  into  which  the 
steam  passes  from  the  boiler ;  c  represents  the  exhaust 
port,  through  which  the  exhaust  steam  passes  out  of  the 
engine.;  di  and  d^  represent  the  steam  ports,  through 
which  the  steam  passes  into  the  cylinder  from  the  steam 
chest.  In  the  figure,  the  valve  is  supposed  to  be  in  mid- 
position  and  is  shown  as  lapping  over  and  beyond  the 
ports,  at  each  end,  a  distance  marked  o  ;  it  is  also  shown 
as  lapping  over  the  ports,  towards  the  inside,  the  distance 
marked  i. 

The  distance  o  is  the  outside  or  steam  lap,  which  is,  the 
distance  the  valve  extends  over  the  edges  of  the  steam  ports 
on  the  outside. 

The  distance  i  is  the  inside  or  exhaust  lap,  which  is,  tJie 
distance  t/ie  valve  extends  over  the  edges  of  the  steam  ports 
on  the  inside. 

In  Fig.  33,  let  C  represent  the  center  of  the  shaft,  and 
A,  the  center  of  the  eccentric  ;  so  that  AC  is  the  eccentri- 
city of  the  eccentric,  and  represents  the  equivalent  crank. 
When  the  valve  is  in  mid-position,  as  shown  in  the  figure, 
the  center  of  the  eccentric  is  at  B,  and  the  valve  has  made 
half  of  its  travel.  While  the  valve  is  in  this  position,  it  is 
evident  that  no  steam  can  enter  or  leave  through  either 
of  the  ports,  d\  or  </2.  If  the  shaft  is  revolved  right- 
handed,  the  valve  will  move  from  its  mid-position  towards 
the  right;  and  when  the  center  of  the  eccentric  has 
reached  any  point  such  as  D,  the  distance  that  the  valve 
will  have  moved  from  mid-position  will  be  equal  to  the 
distance,  CE,  from  the  center  of  the  shaft  to  the  line  DE, 
which  is  drawn  perpendicular  to  AC.  If,  when  the  cen- 
ter of  the  eccentric  gets  to  D,  the  distance  CE  is  equal  to 
o,  the  outside  lap,  the  steam  will  be  just  on  the  point  of 
entering  the  port  d\.  Now,  as  the  shaft  continues  to 
revolve,  the  valve  will  continue  to  move  towards  the  right, 
and  become  farther  and  farther  from  mid-position.  As 


80 


STEAM   ENGINES    AND    BOILERS. 


the  port  was  just  about  to  open   when  the  center  of  the 
eccentric  was  at  Dy  it  is  evident  that  when  the  center  of 


the  eccentric  is  at  any  point  such  as  Di,  beyond  D,  and 
the  valve  has  moved  the  distance  CE±  from  mid-position, 


ADMISSION   OF   STEAM   BY   VALVES.  81 

the  port  has  been  opened  the  amount  EE\y  equal  to 
CEi  —  CE.  When  the  center  of  the  eccentric  gets  to  the 
point  Fy  the  valve  will  have  reached  the  end  of  its  travel 
and  will  be  the  distance  CF  from  mid-position ;  the  port 
will  be  open  the  amount  EF,  equal  to  CF —  CE.  As  the 
shaft  continues  to  revolve,  the  center  of  the  eccentric  will 
move  from  .F  towards  G,  and  the  valve  will  move  towards 
the  left  and  gradually  close  the  port.  When  the  center 
of  the  eccentric  has  gotten  to  the  point  G,  such  that  the 
distance,  CE,  of  the  valve  from  mid-position  is  equal  to  oy 
the  outside  or  steam  lap,  the  port  will  be  just  closed. 
When  the  center  of  the  eccentric  has  reached  the  point 
B\t  the  valve  will  again  be  in  mid-position  ;  and  when  it 
has  gotten  to  A,  the  valve  will  have  reached  the  end  of 
its  travel  towards  the  left. 

It  is  evident,  from  the  figure,  that  no  motion  of  the 
valve  towards  the  left  of  mid-position  can  open  the  port 
d\  to  the  space  a  of  the  steam  chest ;  and,  as  the  valve  is 
always  to  the  left  of  mid-position  while  the  center  of  the 
eccentric  is  anywhere  on  the  arc  B\  ABt  it  follows  that 
the  port  d\  cannot  be  open  to  the  steam  chest  while  the 
center  of  the  eccentric  moves  from  B\  to  B.  As  it  has 
been  shown  that  the  port  d\  is  open  only  while  the  center  of 
the  eccentric  moves  over  the  part  DG  of  the  arc  BFBi,  it 
follows  that,  during  one  revolution  of  the  shaft,  the  port  d\ 
is.  open  only  during  the  time  that  the  center  of  the 
eccentric  moves  from  D  to  G. 

It  is  evident,  from  the  figure,  that  the  larger  is  the  out- 
side lap,  equal  to  the  distance  CE,  the  smaller  is  the  arc  DG; 
and  the  smaller  is  the  lap,  the  larger  is  the  arc  DG.  If 
the  outside  lap  were  zero,  the  port  would  remain  open 
during  half  a  revolution  of  the  eccentric,  or  while  the 
center  of  the  eccentric  traveled  over  the  arc  BFB\. 

Referring  again  to  Fig.  33,  let  us  discuss  the  opening 
and  the  closing  of  the  port  d\  to  the  exhaust  port  c,  during 
one  revolution  of  the  shaft. 
6 


82  STEAM   ENGINES    AND    BOILERS. 

From  the  figure,  it  can  be  seen  that  no  movement  of 
the  valve  towards  the  right  of  the  mid-position  will  open 
di  to  c,  and,  therefore,  at  no  time  during  the  motion  of 
the  center  of  the  eccentric  from  B  to  B\  is  the  port  d\  in 
communication  with  c.  When  the  center  of  the  eccen- 
tric gets  to  B\  the  valve  is  again  in  midposition,  and  as  it 
continues  to  revolve,  the  valve  moves  towards  the  left. 
When  the  center  of  the  eccentric  gets  to  the  point  //,  such 
that  the  distance  CK  is  equal  to,  z,  the  inside  or  exhaust 
lap,  the  port  di  is  just  on  the  point  of  opening  to  the 
exhaust  port,  c.  As  the  motion  of  the  eccentric  con- 
tinues, the  port  becomes  more  and  more  open  to  c; 
and  when  the  center  of  the  eccentric  has  reached  any 
point  such  as  Z,  the  port  d\  is  open  to  c  the  amount  KK\t 
equal  to  CK\ —  CK.  When  the  center  of  the  eccentric 
gets  to  At  the  valve  is  at  the  end  of  its  travel  towards  the 
left;  and  as  the  center  continues  to  revolve,  the  valve 
moves  toward  the  right,  and  the  opening  of  the  port  d\  to 
the  exhaust  port,  c,  becomes  smaller  and  smaller  until, 
when  the  center  is  at  Hi,  where  the  distance  CK\s  equal 
to  the  exhaust  lap,  the  communication  of  d\  with  c  is 
closed. 

From  what  has  been  said,  it  is  now  easy  to  follow  the 
various  openings  and  closings  of  d\  during  one  revolution 
of  the  shaft.  Let  us  start  with  the  valve  in  mid-position, 
and  the  center  of  the  eccentric  at  B,  and  consider  the 
shaft  as  revolving  right-handed.  When  the  center  of  the 
eccentric  gets  to  D,  the  port  d\  is  opened  to  the  steam 
space  a,  so  that  steam  may  enter  the  cylinder,  and  it  con- 
tinues open  until  the  point  G  is  reached.  During  the 
movement  of  the  center  of  the  eccentric  from  G  to  H 
the  port  d\  is  closed,  and  no  steam  can  enter  from  a  nor 
leave  by  the  exhaust  port,  c ;  but  at  H  the  port  di  is 
opened  to  c>  so  that  the  steam  may  leave  the  cylinder, 
and  it  continues  open  until  Hi  is  reached. 


ADMISSION    OF    STEAM   BY   VALVES.  83 

It  is  usual  to  say  the  steam  port  is  open,  when  d\  is  open 
to  a;  and  to  say  the  exhaust  port  is  open,  when  d\  is 
opened  to  c. 

By  an  analysis  similar  to  that  made  for  the  port  d-^  it 
can  be  shown  that,  during  one  revolution  of  the  shaft,  the 
port  d<i  is,  also,  open  once  for  the  admission  of  steam  and 
once  for  its  exhaust;  the  difference  between  the  two  ports 
is  that  di  would  be  open  for  the  admission  of  steam  dur- 
ing the  semi-revolution  B\  AB,  instead  of  the  semi-revolu- 
BFB\t  and  would  be  open  for  its  exhaust  during  the 
semi-revolution  BFB\y  instead  of  the  semi-revolution 
BiAB. 

38.  RELATIVE  MOVEMENTS  OF  THE  PISTON.  AND  VALVE. — 
In  Fig.  34,  the  piston  is  shown  at  the  left-hand  end  of 
the  cylinder,  ready  to  begin  its  stroke  toward  the  right ; 
and  the  valve  is  shown  in  such  a  position  that  the  steam 
port  is  open  by  the  amount  marked  /.  The  shaft  is  rep- 
resented by  two  points,  C  and  C\.  C  is  the  center  of 
the  crank  shaft ;  CD  is  the  crank  ;  and  the  circle  DGHF 
is  the  circle  described  by  the  crank-pin  during  one  revo- 
lution. C\  represents,  also,  the  center  of  the  shaft,  and 
the  circle  A\D^G\H±  is  the  circle  described  by  the  center 
of  the  eccentric  during  one  revolution  of  the  shaft.  Of 
course,  C  and  C\  ought  to  coincide,  as  they  both  repre- 
sent the  center  of  the  same  shaft ;  they  are  put  one  above 
the  other,  as  shown,  simply  to  avoid  confusion  in  the 
drawing,  and  for  the  sake  of  clearness. 

The  steam  port  is  open  the  amount  /,  and  the  steam  is 
entering  the  cylinder  to  the  left  of  the  piston.  The  center 
of  the  eccentric  is  at  the  point  D\t  and  the  crank-pin  is 
on  the  dead  center  at  D.  The  shaft  is  supposed  to  revolve 
right-handed,  as  in  Art.  37. 

The  distance  /  is  the  lead,  which  may  be  defined  as 
the  amount  the  steam  port  is  open  when  the  piston  is  at  the 
beginning  of  its  stroke. 


84  STEAM    ENGINES    AND    BOILERS. 

As  the  crank  and  the  eccentric  are  both  fixed  to  the 
shaft,  they  must  preserve  the  same  relative  positions  ;  and 
the  center  of  the  eccentric  will  always  be  ahead  of  the 
crank-pin,  by  the  angle  D\  C\  A\. 

The  angle  B\  C\  D\  is  the  angle  of  advance,  equal  to 
D\  C\  AI  —  90,  and  is  defined  as  the  angle  the  center  line 
of  the  eccentric  makes  with  a  perpendicular  to  the  line  of 
motion  of  the  piston,  when  the  crank  is  on  the  dead 
center. 

If  we  make  C\  N  equal  to  the  steam  lap,  and  C\  K 
equal  to  the  exhaust  lap,  and  draw  the  lines  F\  G\  and 
LI  H\  perpendicular  to  A\  C\  and  intersecting  the  circle 
at  the  points  F\,  G\,  Li,  and  H\,  we  shall  have,  from  the 
reasoning  of  Art.  37,  the  point,  F\,  at  which  the  center  of 
the  eccentric  is  when  the  steam  port  is  opened  ;  the  point, 
GI,  at  which  the  steam  port  is  closed ;  the  point,  H\,  at 
which  the  exhaust  port  is  opened  ;  and  the  point,  L\t  at 
which  the  exhaust  port  is  closed.  Since  C\  A7"  is  equal  to 
the  steam  lap,  o,  of  the  valve,  and  C\  R  is  the  distance 
the  valve  is  from  mid-position  when  the  center  of  the 
eccentric  is  at  D\,  it  follows  that  the  lead,  /,  is  equal  to 
Ci  R  —  Ci  N;  and  Ci  R  =  o  +  /.  And  as  Ci  R  is  the 
distance  the  valve  has  moved  from  mid-position  while  the 
eccentric  turns  through  the  angle  B\  C\  D\,  it  follows  that 
the  angle  of  advance  is  the  angle  through  which  the  eccen- 
tric must  be  turned  in  order  to  move  the  valve  from  mid- 
position  a  distance  equal  to  the  steam  lap  plus  the  lead. 

Therefore,  for  a  given  steam  lap  of  valve  and  a  given 
eccentricity,  the  greater  the  angle  of  advance  is  made,  the 
greater  becomes  the  lead  ;  and  the  less  the  angle  of 
advance  is  made,  the  less  becomes  the  lead.  If  the  angle 
of  advance  is  equal  to  the  angle  B\  C\  F\,  the  lead  would 
be  zero  and  the  valve  would  be  said  to  be  "  blind  ;  "  if  the 
angle  of  advance  should  be  less  than  the  angle  B\  C\  F\ 
C\  R  would  be  less  than  C\  N9  and  the  lead  would  be 
negative.  Again,  for  a  given  lead  and  eccentricity,  the 


ADMISSION   OF  STEAM   BY   VALVES. 


85 


86  STEAM    ENGINES    AND    BOILERS. 

angle  of  advance  will  be  increased,  if  the  steam  lap  is 
increased;  and  be  decreased,  if  the  steam  lap  is  decreased. 

In  finding  the  position  of  the  crank  for  different  posi- 
tions of  the  eccentric,  we  start  with  the  position,  D,  of 
the  crank  when  the  eccentric  is  at  D\,  and,  as  their 
positions  relative  to  one  another  are  fixed,  we  know  that 
they  must  both  turn  through  the  same  angle  in  the  same 
time.  The  position,  G,  of  the  crank-pin  when  the  steam 
port  is  closed,  is  obtained  by  making  the  angle  DCG 
equal  to  the  angle  D\  Ci  G\.  From  the  figure  it  is  seen  ' 
that  the  greater  the  angle  of  advance  becomes,  for  a 
valve  with  a  given  steam  lap,  the  less  becomes  the  angle 
D\  Ci  GI  and  its  equal,  DCG,  and,  therefore,  the  earlier 
will  be  the  point  ofcut-off;  also,  the  larger  the  steam  lap, 
the  less  is  the  angle  FI  C\  Gi,  and,  therefore,  for  a  given 
lead,  the  less  will  be  the  angle  Di  Ci  Gi  and  its  equal, 
DCG,  and  the  earlier  will  be  the  cut-off.  From  this 
follows  a  general  proposition,  which  always  holds  for  the 
slide  valve,  as  follows,  the  greater  the  angle  of  advance, 
for  a  given  eccentricity  and  steam  lapy  the  greater  will  be 
the  lead,  and  the  earlier  will  be  the  cut-off;  the  greater  the 
steam  lap,  for  a  given  eccentricity  and  lead,  the  greater  will 
be  the  angle  of  advance,  and  the  earlier  will  be  the  cut-off. 

To  find  the  position,  //,  of  the  crank-pin  when  the 
exhaust  port  opens,  or  release  occurs,  make  GCH  equal 
to  G\  C\  H\,  or  make  Z>£7/equal  to  D\  C\  H\.  Anything 
that  will  make  the  angle  D\  C\  H\  or  its  equal,  DCHt 
smaller  will  make  the  release  occur  earlier.  Now,  increas- 
ing the  angle  of  advance  throws  Di  farther  towards  //i, 
and  decreases  the  angle  D\  C\  H\\  increasing  the  exhaust 
lap,  C\  K,  throws  Hi  farther  towards  A\,  and  increases  the 
angle  D\  C\  H\.  It  follows,  therefore,  that,  for  a  given 
eccentricity  and  exhaust  lap,  increasing  the  angle  of 
advance  makes  the  release  occur  earlier ;  and,  for  a  given 
angle  of  advance  and  eccentricity,  increasing  the  exhaust 
lap  makes  the  release  occur  later. 


ADMISSION    OF    STEAM    BY   VALVES.  87 

The  position,  L,  of  the  crank-pin  when  compression 
begins,  or  the  exhaust  port  closes,  is  best  obtained  by 
making  the  small  angle  D  C  L,  below  DC,  equal  to  the 
small  angle  D\C\L\.  Anything  that  causes  the  angle 
DI  Ci  LI  to  be  large,  will  make  the  point  L  be  farther  from 
D,  and  will  make  the  compression  begin  earlier.  The 
angle  D\  C\  LI  may  be  increased  by  making  the  angle  of 
advance,  £i  C\  D\,  greater  or  by  increasing  the  exhaust 
lap,  thus  throwing  L\  farther  towards  A\.  It  follows, 
then,  that,  for  a  given  eccentricity  and  exhaust  lap,  an 
increase  in  the  angle  of  advance  makes  the  compression 
begin  earlier;  and,  for  a  given  eccentricity  and  angle  oj 
advance,  an  increase  in  the  exhaust  lap  makes  the  com- 
pression begin  earlier. 

Finally,  the  position,  F,  of  the  crank-pin  when  admis- 
sion begins,  or  the  steam  port  is  opened,  is  obtained  by 
laying  off,  below  D  C,  the  angle  D  C  F equal  to  the  angle 
D\  C\F\.  It  is  evident,  from  the  figure,  that,  for  a  given 
eccentricity  and  steam  lap,  an  increase  in  the  angle  of 
advance  makes  the  admission  occur  earlier;  and,  for  a 
given  eccentricity  and  angle  of  advance,  an  increase  in  the 
steam  lap  makes  the  admission  occur  later. 

It  will  be  noticed,  from  what  has  been  explained,  that, 
for  a  given  eccentricity,  steam  lap,  and  exhaust  lap,  an 
increase  in  the  angle  of  advance  makes  the  lead  greater, 
and  makes  the  ports  open  and  close  earlier. 

When  the  positions  of  the  crank-pin  are  known  for  the 
different  positions  of  the  valve,  it  is  very  easy  to  deter- 
mine the  positions  of  the  piston,  provided  the  obliquity  of 
the  connecting  rod  is  neglected,  since  the  distance  the 
piston  is  from  the  beginning  of  its  stroke  is  always  equal 
to  the  distance  from  the  dead  center  to  the  perpendicular 
let  fall,  on  the  line  of  motion  of  the  piston,  from  the  cen- 
ter of  the  crank-pin.  Thus,  when  the  crank-pin  is  at  G, 
the  piston  is  at  the  distance  Dg  from  the  beginning  of  its 


88  STEAM    ENGINES    AND    BOILERS. 

Since  G  is  the  position  of  the  crank-pin  when  cut-off 
takes  place,  g  is  the  "  point  of  cut-off,"  and  Dg  expressed 
as  a  fraction  of  the  stroke  is  the  "  cut-off." 

That  point  in  the  stroke  at  which  the  piston  is  when  the 
exhaust  port  is  opened,  is  called  the  "  point  of  release;  " 
that  point  in  the  stroke  at  which  the  piston  is  when  the 
exhaust  port  is  closed,  is  the  "  point  of  compression  ; " 
and  that  point  in  the  stroke  at  which  the  piston  is  when 
the  steam  port  is  opened,  is  called  the  "  point  of  admis- 
sion.'* The  "point  of  cut-off"  has  already  been  defined. 

The  positions  of  the  piston  at  the  times  of  the  opening 
and  closing  of  the  ports  are  indicated  on  the  drawing,  g 
is  the  point  of  cut-off;  h,  the  point  of  release  ;  i,  the  point 
of  compression ;  and  /,  the  point  of  admission.  We  are 
now  able  to  trace  the  motion  of  the  piston  and  note  the 
action  of  the  steam.  The  piston  starts  at  the  left  end  of 
its  stroke  and  moves  towards  the  right,  with  steam  enter- 
ing the  cylinder  during  the  whole  time ;  at  g  the  steam  is 
cut-off,  and  while  the  piston  moves  to  h,  from  g,  the  steam 
remaining  in  the  cylinder  is  being  expanded.  At  h 
release  occurs ;  the  steam  begins  to  leave  the  cylinder 
and  continues  to  leave  until  the  piston  gets  to  it  on  its 
return  stroke.  At  i  the  exhaust  port  is  closed,  and  the 
steam  remaining  in  the  cylinder  is  compressed  while  the 
piston  moves  from  i  to  ft  on  the  return  stroke.  Atf  the 
steam  port  is  opened,  and  steam  begins  to  enter  the 
cylinder. 

The  same  kind  of  analysis  can  be  followed  out  for  the 
steam  entering  the  cylinder  to  the  right  of  the  piston. 
The  'point  of  cut-off,  of  release,  of  compression,  and  of 
admission,  will  be  the  same  distance  from  the  end  of  the 
stroke ;  everything  will  be  the  same  except  that  the 
points  of  cut-off  and  release  will  occur  while  the  piston  is 
moving  from  right  to  left,  and  the  points  of  compression 
and  admission  will  occur  while  the  piston  is  moving  from 
left  to  right. 


ADMISSION    OF    STEAM   BY   VALVES. 


89 


39.  BALANCED  SLIDE  VALVE. —  In  order  to  avoid  the 
friction  of  the  plain  .D-valve,  such  as  shown  in  Figs.  33 
and  34,  where  the  full  pressure  of  the  steam  presses  the 
valve  against  its  seat,  and  makes  it  difficult  to  move,  some 
form  of  balanced  valve  is  generally  used  on  automatic 
high  speed  engines.  A  balanced  valve  not  only  requires 
less  power  to  move  it,  but  also  wears  less  than  an  unbal- 
anced valve. 

The  general  form  of  balanced  slide  valve  in  common 
use  is  the  "  Straight  Line  "  valve,  or  some  modification 
of  it.  This  valve  is  shown  in  Figs.  35  and  36.  It  will  be 
seen  that  the  valve  is  simply  a  flat  casting,  a,  with  open- 


Fig.  35. 

ings  through  it,  that  moves  back  and  forth  between  the 
valve  seat  and  a  "  cover-plate,"  b.  The  cover-plate  does 
not  rest  directly  on  the  valve  but  on  "  distance-pieces," 
cy  at  the  top  and  bottom  of  the  valve.  The  cover-plate  is 
sometimes  kept  in  place  by  means  of  springs,  interposed 
between  it  and  the  steam  chest  cover;  other  times  the 
valve  is  not  set  exactely  vertical,  but  is  slightly  inclined, 
so  that  the  weight  of  the  valve  and  cover-plate  is  suffi- 
cient to  keep  it  in  place.  The  valve  shown  in  Figs.  35 
and  36  has  no  special  means  of  correcting  for  the  wear 
of  the  valve ;  the  only  way  to  do  this  is  to  reduce  the 
thickness  of  the  distance  pieces,  c.  Some  valves  are  pro- 
vided with  wedges,  by  means  of  which  the  distance  pieces 


90 


STEAM   ENGINES    AND    BOILERS. 


may  be  set  out  and  the  cover-plate  lifted  any  desired 
distance  from  the  valve.  Fig.  35  shows  steam  being  ad- 
mitted to  the  right-hand  end  of  the  cylinder  and  being  ex- 
hausted from  the  left-hand  end,  as  indicated  by  the  arrows. 

40.  PISTON  VALVE. —  The  piston  valve  consists  simply 
of  a  piston  working  in  a  cylinder  through  which  the  ports 


Fig.  36. 

are  cut.  The  length  of  the  port  is  equal  to  the  circum- 
ference of  the  piston,  less  the  width  of  such  ribs  as  may 
extend  across  the  port.  This  form  of  valve  is  perfectly 
balanced,  but  it  is  difficult  to  keep  it  tight  and  prevent 
it  from  leaking.  When  steam  is  first  turned  on  to  an 


ADMISSION    OF    STEAM   BY    VALVES.  91- 

engine  having  a  piston  valve,  care  must  be  taken  not  to 
start  it  up  until  the  steam  chest  has  got  thoroughly  hot, 
as  the  valve  is  very  likely  to  become  hot  before  the  cylin- 
der in  which  it  works,  and  to  expand  and  stick,  and  per- 
haps cause  a  breakage  somewhere. 

The  piston  used  for  the  valve  is  sometimes  made  tight 
by  the  use  of  cast  iron  packing  rings,  other  times  it  is 
simply  turned  to  a  steam  tight  fit  with  the  cylinder  in 
which  it  works. 

In  Fig.  15  is  shown  a  form  of  piston  valve  where  the 
cylinder  in  which  the  valve  fits  is  made  with  thin  walls 
and  is  surrounded  by  live  steam,  so  that  it  heats  quicker 
than  the  valve  and  there  is  not  so  much  danger  of  the 
valve  sticking.  The  figure  shows  steam  being  admitted  to 
the  right-hand  end  and  exhausted  from  the  left-hand  end. 

41.  MULTIPLE  ADMISSION    VALVE. —  With  the  advent 
of  the  automatic  high  speed  engine,  there  came  a  demand 
for  a  single  valve  which  could   be   made  to  cut-off  early 
in  the  stroke  and  that   would  give  a  large  port-opening 
with  a  small  travel.     To    meet   these  requirements,  the 
multiple  admission   valve  was    devised.     Valves    of  this 
type  are  so  made   that  the  opening  of  the  port  is  not,  as 
shown  in  Art.  37,  equal  to  the  distance  the  valve  is  from 
mid-position  minus    the    steam   lap,  but  is  equal  to  two 
times  this  distance  for  a  double  admission  valve,  and  four 
times  it  for  a  quadruple  admission  valve. 

The  "Straight  Line"  valve,  shown  in  Figs.  35  and  36, 
is  a  double  admission  valve. 

42.  MEYER  VALVE.  —  The  Meyer  valve  consists  of  two 
valves,  one  riding  on  top  of  the  other;  and  the  advantages 
it  has  over  the  single  valves  are  that  the  clearance  may  be 
made  smajler,  and  the  point  of  cut-off  may  be  changed 
as   desired  without  in  any  way  changing  the  points  of 
release  or  compression,  something  which  cannot  be  done 
with  a  single  valve.     The  valve  shown  in  Fig.  17  is  a  mod- 
ified form   of  a  Meyer  valve.     It   consists  of    the  main 


92  STEAM    ENGINES    AND    BOILERS. 

valve  b,  moved  backwards  and  forwards  by  a  hollow  valve 
stem,  and  the  small  auxiliary  valve  c,  which  rides  on  b, 
and  is  moved  by  a  small  valve  stem  working  inside  of  the 
hollow  valve  stem  which  moves  b.  In  order  that  steam 
may  enter  the  cylinder,  the  port  in  b  must  not  be  covered 
by  c,  and  it  must  be  over  the  port  in  the  cylinder.  In 
the  figure  steam  is  being  admitted  into  the  left-hand  end 
of  the  cylinder  and  exhausted  from  the  right-hand  end,  as 
indicated  by  the  arrows.  D  is  the  steam  supply  pipe,  and 
Kt  the  exhaust  pipe.  The  cut-off  is  regulated  entirely  by 
the  small,  riding  valve  c,  while  the  admission,  release,  and 
compression  are  regulated  entirely  by  the  main  valve  b. 

43.  CORLISS  VALVE. —  The  Corliss  valve  is  a  cylindrical 
valve,  but  instead  of  having  a  reciprocating  motion  in  the 
direction  of  its  axis,  it  has  an  oscillating  motion  about  its 
axis.  In  Figs.  19  and  37  are  shown  Corliss  valves.  It 
will  be  seen,  in  Fig.  19,  that  there  are  four  valves  in  all, 
two  steam  valves  at  the  top  of  the  cylinder,  and  two 
exhaust  valves  at  the  bottom.  The  valves  are  not  fast- 
ened to  the  stem  by  which  they  are  moved,  but  the  stem 
is  flattened  and  simply  lies  in  the  valve.  The  valves  are 
always  made  so  that  the  steam  pressure  comes  on  top  of 
them  and  the  pressure  of  the  steam  presses  them  down  on 
their  seats.  The  moving  mechanism  of  the  valves  is  quite 
complicated,  and  has  many  small  parts  that  must  be  kept 
in  order. 

The  clearance  is  reduced  by  making  the  ports  very 
short  and  placing  the  valve  close  to  the  cylinder. 

The  Corliss  valve  permits  a  regulation  of  the  point  of 
cut-off  without  any  change  in  the  release  or  compression. 

As  there  are  separate  steam  and  exhaust  ports,  the 
exhaust  steam  does  not  pass  out  through  the  same  port 
through  which  the  hot,  live  steam  enters.  Whether  or 
not  this  is  any  advantage,  and  conduces  to  the  economy 
of  the  engine,  is  a  somewhat  undecided  question.  In  Fig. 


ADMISSION    OF    STEAM    BY    VALVES. 


93 


37  is  shown  the  mechanism  by  means  of  which  the  valves 
of  the  Corliss  engine  are  worked. 


The  "wrist-plate,"  A,  is  made  to  oscillate  about  the 
pin  B,  by  means  of  the  "  reach-rod,"  C,  which  engages 
with  the  "  wrist-pin."  The  wrist-plate  is  connected  by 
the  rod  D  to  the  bell  crank,  £,  that  oscillates  about  the 


94  STEAM    ENGINES    AND    BOILERS. 

N 

valve  stem  F.  At  the  farther  end  of  E  is  the  pin  G  which 
carries  the  F-shaped  lever  H.  The  inner  end  of  H  is 
kept  pressed  against  the  cam  /  by  means  of  a  spring ; 
and  the  outer  end  has  a  hook  which  engages  with  a  steel 
block  fastened,  by  means  of  the  bolt  K,  to  an  arm,  Z, 
rigidly  attached  to  the  valve  stem  F.  The  dash  pot  rod, 
Mt  is,  also,  attached  to  the  arm  L.  The  cam  /has  a  pro- 
jection on  it,  and  is  moved  backward  or  forward  by  means 
of  the  governor  rod,  not  shown  in  the  figure,  that  is 
attached  to  the  pin  O. 

When  the  wrist-plate  is  turned  right-handed  the  crank 
E  is  turned  left-handed,  and  the  hook  on  //"engages  with 
the  block  on  Kt  and  thus  lifts  the  lever  L  and  opens  the 
valve.  When  L  is  lifted,  the  dash-pot  rod,  M,  is  lifted. 
After  the  lever  L  has  been  lifted  to  a  certain  distance, 
the  inner  end  of  //"strikes  the  projection  on  the  cam  /, 
which  turns  H  about  the  pin  G,  so  that  the  hook  is 
released  from  the  block  K.  As  soon  as  this  takes  place, 
the  arm  L  is  made  to  fall,  by  the  weight  of  the  dash-pot 
piston  and  the  pressure  of  the  air  on  top  of  the  piston, 
and  thus  close  the  valve.  The  function  of  the  dash-pot 
is  to  close  the  valve ;  and  it  is  so  arranged  that  by  means 
of  a  small  valve  a  greater  or  less  vacuum  may  be  main- 
tained under  its  piston. 

The  governor  changes  the  position  of  the  cam  /so  that 
the  block  K  is  disengaged  early  or  late,  as  required  to 
govern  the  engine,  from  the  hook  on  H. 

The  exhaust  valves  have  no  disengaging  mechanism, 
but  are  simply  made  to  oscillate  backward  and  forward 
by  means  of  a  rod  connecting  them  to  the  wrist-plate. 

Owing  to  this  peculiar  method  of  closing  the  valve,  the 
speed  of  rotation  of  the  engine  cannot  be  great,  as  the 
dash-pot  piston  must  have  time  in  which  to  fall.  The 
writer  has  known  of  but  few  cases  where  the  number  of 
revolutions  has  exceeded  one  hundred  per  minute,  and 
in  most  cases  the  engines  were  small. 


ADMISSION    OF    STEAM    BY    VALVES. 


(J5 


The  advantages  claimed  for  Corliss  valves  are :  — 

I.  They  permit  of  a  regulation  of  the  cut-off  without 
any  change  in  the  release  or  compression. 


Fig.  38 

2.  Short    ports,    and,   consequently,    small    clearance 
volume. 

3.  Separate  steam    and  exhaust  ports,    reducing  con- 
densation. 


96  STEAM    ENGINES    AND    BOILERS. 

4.  Quick,  sharp,  motion  of  the  valve  when  cutting  off 
steam. 

44.  LINK  MOTION.  —  On  marine  engines,  locomotives, 
and  some  few  land  engines,  it  is  necessary  to  have  some 
device  by  which  the  direction  of  rotation  of  the  crank-shaft 
may  be  changed.  The  mechanism  usually  used  is  the 
link  motion.  The  engine  is  provided  with  two  eccentrics, 
keyed  to  the  crank-shaft,  each  of  which  is  connected  by 
an  eccentric  rod  to  the  end  of  a  link.  A  block,  connected 
by  a  suitable  mechanism  to  the  valve,  slides  along  a 
groove  cut  in  the  link.  When  the  block  is  at  one  end  of 
the  link  it  has  all  the  motion  of  the  eccentric  connected 
to  that  end,  and  very  little  of  the  motion  of  the  other 
eccentric  ;  when  the  block  is  in  the  middle  of  the  link  it  has 
a  little  motion,  backward  and  forward,  that  is  the  result 
of  the  motions  of  both  eccentrics.  One  of  the  eccentrics 
is  the  "  forward  "  eccentric,  and  the  other  is  the  "  back- 
ward "  eccentric.  When  the  motion  of  the  valve,  on 
account  of  the  position  of  the  block,  is  due  more  to  the 
"  forward  "  than  to  the  "  backward  "  eccentric,  the  engine 
runs  forward  ;  and  when  influenced  more  by  the  "back- 
ward "  than  the  "  forward  "  eccentric,  the  engine  will  run 
backward.  The  position  of  the  block  in  the  link  may  be 
changed  by  moving  the  block  and  keeping  the  link  in  the 
same  position ;  or  by  keeping  the  block  at  rest  and 
moving  the  link,  as  is  done  in  the  Stephenson  link 
motion. 

In  Fig.  38  is  shown  a  small  vertical  engine  with  a  link 
motion.  A  is  the  "  link;  "  B  is  the  "  block"  that,  in  this 
case,  is  fastened  directly  to  the  valve  stem ;  C  is  the 
"  reversing  lever"  by  means  of  which  the  link  is  moved  so 
that  the  position  of  the  block  in  it  may  be  changed. 


CHAPTER    V. 

VALVE    DlAGRAMSo 

45.  ZEUNER  VALVE  DIAGRAM. —  A  valve  diagram  is  a 
diagram  that  will  show,  at  once,  the  steam  lap,  exhaust 
lap,  lead,  distance  the  valve  is  from  mid-position,  and, 
also,  the  amount  the  port  is  open  for  a  given  position  of 
the  crank.  By  means  of  valve  diagrams,  all  the  various 
problems  connected  with  the  motion  of  valves  may  be 
solved.  There  are  several  systems  of  valve  diagrams, 
each  of  which  is  considered  better  than  the  others  by  those 
who  use  it ;  and  as,  in  the  opinion  of  the  author,  the 
Zeuner  diagram  is  better  for  all  uses  than  any  other,  it 
will  be  used  in  this  work. 

In  Fig.  39,  let  AA'  represent  the  stroke  of  an  engine 
drawn  to  any  desired  scale,  and  the  circle  ABA',  the  path 
of  the  center  of  the  crank  pin,  or  the  crank-circle.  Also, 
let  nm  be  the  travel  of  the  valve  drawn  to  any  desired 
scale,  which  may  or  may  not  be  the  same  as  the  scale  of 
AA'.  The  distance  On  will  be  equal  to  the  eccentricity 
of  the  eccentric,  and  the  circle  nAi  m  will  be  the  path  of 
the  center  of  the  eccentric.  When  the  crank-pin  is  at  At 
the  center  of  the  eccentric  will  be  at  Ai,  and  YOA\  will 
be  the  angle,  of  advance.  Now,  if  the  crank  moves  from 
AO  to  any  position  as  BO,  the  center  of  the  eccentric 
will  move  from  A\  to  Bi,  and  the  angle  AOB  will  be 
equal  to  the  angle  AiOBi.  Draw  B\b  perpendicular  to 
the  line  AA ;  then,  neglecting  the  obliquity  of  the  eccen- 
tric rod,  when  the  crank  is  in  the  position  BO,  the  valve 
will  be  moved  from  mid-position  a  distance  equal  to  Ob. 
To  find  the  distance  Ob  by  the  method  just  described,  it 

r  (97) 


98 


STEAM    ENGINES    AND    BOILERS. 


was  necessary  to   draw  three  lines,   OB,  OB\,    and  Bib, 
and  to  make  the  angle  A\OB^  equal  to  the  angle  AOB. 

Draw  OB'  so  that  the  angle  B'OA'  will  be  equal  to  the 
angle  BOA,  and  H  O  will  be  the  position  of  an  imaginary 
crank  which  starts  from  A  O  when  the  real  crank  starts 
from  AO  and  moves  with  the  same  velocity  as,  but  in 


Fig.  39. 

the  opposite  direction  to,  the  real  crank.  Draw  A\a  per- 
pendicular to  OB' .  In  the  two  right  triangles,  OB\b  and 
OAia,  we  have  OAi  equal  OB\,  and  the  angle  B\0b  equal 
the  angle  A\0a.  Therefore,  the  two  triangles  are  equal, 
and  Oa  is  equal  to  Ob  :  or  Oa  is  equal  to  the  distance  the 
valve  is  from  mid-position  when  the  crank  has  moved 
through  the  angle  AOB,  equal  to  A  OB'.  From  this,  it 
is  seen  that  if,  instead  of  considering  the  real  crank,  we 
consider  the  motion  of  an  imaginary  crank  revolving  in 
the  opposite  direction  to,  but  with  the  same  velocity  as, 
the  real  crank,  the  distance  that  the  valve  is  from  mid- 
position,  for  a  given  angular  motion  of  the  crank,  may  be 
obtained  by  drawing  only  two  lines,  OB'  and  A\a. 


VALVE    DIAGRAMS.  D9 

Since  the  position  of  the  point  AI  is  fixed,  for  a  given 
eccentricity  and  angle  of  advance,  and  the  angle  A\aO  is 
a  right  angle,  the  point  a  will  always  fall  upon  the  circum- 
ference of  the  circle  drawn  upon  OA\  as  a  diameter.  This 
gives  us,  then,  an  extremely  simple  means  of  obtaining 
the  distance  the  valve  is  from  mid-position  after  the  crank 
has  moved  through  any  given  angle. 

In  Fig.  40,  let  AA't  as  before,  represent  the  stroke  of 
the  engine,  and  ADBA'  the  path  of  the  crank-pin;  also, 
let  the  angle  YOA\  be  the  angle  of  advance ;  and  let  OA\ 
be,  to  any  desired  scale,  the  eccentricity  of  the  eccentric, 
equal  to  half  the  travel  of  the  valve.  Upon  OA\9  as  a 
diameter,  draw  the  "valve  circle  "  OaA^.  From  the  pre- 
ceding paragraph,  it  follows  that  if  OB  represents  any 
position  of  the  imaginary  crank,  at  any  instant,  Ob  will 
represent  the  distance  the  valve  is  form  mid-position  at 
that  instant.  That  is,  by  drawing  one  line  we  determine, 
at  once,  the  angle  the  crank  has  turned  through  and  the 
distance  the  valve  is  from  mid-position.  Care  must  be 
taken  to  remember  that  OB  does  not  represent  the  real 
crank  of  the  engine,  but  an  imaginary  crank  that  revolves 
with  same  velocity  as  the  real  crank,  but  in  the  opposite 
direction. 

Neglecting  the  obliquity  of  the  connecting  rod,  the  dis- 
tance the  piston  would  have  moved  from  the  end  of  its 
stroke,  while  the  crank  moved  through  an  angle  equal  to 
A' OB,  would  be  B^A '.  And  if,  as  we  supposed,  the  real 
crank  moved  in  the  direction  from  A  to  Yt  the  piston 
would  have  moved  the  distance  B\A'  from  the  left-hand 
end  of  the  stroke  and  not  from  the  right-hand  end. 

If  we  describe  the  arc  dcy  with  O  as  a  center  and  a 
radius  equal  to  the  outside  or  steam  lap  of  the  valve,  the 
distance  the  steam  port  is  open,  when  the  crank  has 
moved  through  the  angle  equal  to  BOA' ,  will  be  equal  to 
Ob  —  Ob' ;  that  is,  it  will  be  equal  to  the  distance  the 
valve  is  frjm  mid-position  minus  the  steam  lap. 


100 


STEAM    ENGINES    AND    BOILERS. 


If  the  lines  OC  and  OD  be  drawn  through  c  and  d, 
respectively,  OC  will  represent  the  position  of  the 
imaginary  crank  when  steam  begins  to  enter  the 
cyclinder,  and  OD  its  position  when  steam  is  cut-off; 
because,  for  those  positions,  the  distance  the  valve  is  from 
mid-position  is  equal  to  the  steam  lap. 

When  the  crank  is  on  the  dead  center,  the  imaginary 
crank  is  at  OA't  and  the  distance  the  valve  is  from  mid- 
position  is  Oa,  so  that  the  lead  is  a' a. 


Fig.  40. 

The  valve  is  open  its  maximum  distance  when  the 
imaginary  crank  is  in  the  position  of  the  line  OA\,  and 
then  the  valve  is  at  the  right-hand  end  of  its  travel. 

If  the  line  DD\  is  drawn  perpendicular  to  AA',  the 
distance  A ' D\  will  be  the  distance  the  piston  is  from  the 
beginning  of  the  stroke  at  the  point  of  cut-off. 

If  the  line    OA\  be   continued  to  ^2,   so    that   OA2  is 


VALVE    DIAGRAMS.  101 


equal  to  OAi,  and  another  valve  circle  be  drawn  on 
as  a  diameter,  the  exhaust  port  may  be  discussed. 
Draw  the  arc  fgt  with  O  as  a  center  and  a  radius  equal  to 
the  exhaust  lap.  Then,  for  any  position  of  the  imaginary 
crank,  such  as  O  K,  the  exhaust  port  is  open  the  distance 
kk\y  equal  "to  the  distance,  Ok,  the  valve  is  to  the  left  of 
mid  position  minus  the  exhaust  lap,  Oki. 

If  OF  and  OG  are  drawn  through  the  points/and  gt 
respectively,  OF  will  be  the  position  of  the  imaginary 
crank  when  release  occurs,  and  OG  its  position  when 
compression  begins  ;  since,  for  those  positions,  the  dis- 
tance the  valve  is  from  mid-position  is  equal  to  the 
exhaust  lap. 

46.  VALVE  DIAGRAM  PROBLEMS.  —  By  assuming  a  num- 
ber of  the  variables.  in  the  valve  diagram,  in  Fig.  40,  as 
known,  various  problems  can  be  made  up,  all  of  which  can 
be  solved  by  the  proper  use  of  the  valve  diagram.  The 
solution  of  every  problem  will  necessitate  a  good,  clear, 
understanding  and  knowledge  of  the  relation  of  the  various 
parts  of  the  diagram  to  one  another.  For  the  sake  of 
making  the  student  familiar  with  the  use  of  the  valve 
diagram  and  to  give  him  practice  in  the  use  of  it,  a  number 
of  the  most  important  problems  likely  to  be  met  with 
in  practice  will  be  solved  in  detail. 

Problem  I.  Given  the  point  of  admission,  the  point  of 
cut-off,  and  the  travel  of  the  valve  ;  find  the  angle  of  ad- 
vance, the  steam  lap,  and  the  lead. 

Referring  to  Fig.  40,  we  see  that  since  Od  is  equal  to 
Oc,  being  the  radii  of  the  steam  lap  circle,  the  arc  Od  is 
equal  to  the  arc  Oc,  and,  therefore,  the  arc  dA\  is  equal  to 
the  arc  cA\.  That  is,  the  line  OA\  bisects  the  angle  between 
the  positions  of  the  imaginary  crank  at  admission  and  at 
cut-off.  The  construction,  therefore,  is  as  follows  :  — 

In  Fig.  41,  let  AA\  be  the  stroke  of  the  engine  drawn  to 
any  desired  scale  ;  A\  B\,  the  distance  from  the  end  of 


102 


STEAM    ENGINES    AND    BOILERS. 


the  stroke  to  the  point  of  admission ;  and  Ai  C\,  the 
distance  from  the  beginning  of  the  stroke  to  the  point  of 
cut-off.  On  A\A  as  a  diameter,  construct  the  crank 
circle  ACA\B.  Draw  the  lines  B\.B  and  C\  C  perpendicu- 
lar toy^iand  intersecting  the  crank  circle  at  B  and  C, 
respectively.  Now  draw  OB  and  OC,  and  they  will  rep- 
resent the  positions  of  the  imaginary  crank  at  admission 
and  cut-off,  respectively.  Draw  Om,  bisecting  the  angle 
COB,  and  lay  off  Om,  according  to  any  desired  scale, 
equal  to  the  given  eccentricity  of  the  eccentric,  or  half 


Fig.  41. 

the  travel  of  the  valve,  m  will  be  the  position  of  the 
center  of  the  eccentric  when  the  real  crank  is  in  the 
position  OA ;  and  the  angle  YQm  will  be  the  required 
angle  of  advance. 

On  Om  as  a  diameter,  draw  the  valve  circle  intersecting 
0 C  at  cy  OA  at  a,  and  OB  at  b.  With  O  as  a  center  and 
a  radius  equal  to  Ocy  equal  Ob,  draw  the  arc  cdb  inter- 
secting OA  at  d.  cdb  is  an  arc  of  the  steam  lap  circle  ;  Ob 
is  the  steam  lap ;  and  da  is  the  lead. 

Problem  2.  Given   the  point  of  admission,  the  point  of 


VALVE    DIAGRAMS. 


103 


cut-off,  and  the  steam  lap  ;  find  the  angle  of  advance,  the 
eccentricity,  and  the  lead. 

An  inspection  of  Fig.  40  shows  that  the  valve  circle 
passes  through  the  points  of  intersection  of  the  steam 
lap  circle  with  the  lines  showing  the  position  of  the 
imaginary  crank  at  admission  and  at  cut-off.  Hence  the 
following  construction  :  — 

In  Fig.  42,  let  AA\  be  the  stroke  of  the  engine,  drawn 
to  any  scale,  and  the  circle  A  CA\B,  the  crank-circle  ;  A\  B\, 
the  distance  of  the  point  of  admission  from  the  end 
of  the  stroke ;  and  A\  C\t  the  distance  of  the  point  of 
cut-off  from  the  beginning  of  the  stroke.  Draw  BB\  and 


Fig.  42. 

CC\  perpendicular  to  AA\  and  intersecting  the  crank- 
circle  at  the  points  B  and  C>  respectively.  Draw  OB  and 
OC  to  represent  the  position  of  the  imaginary  crank  at 
admission  and  cut-off,  respectively.  With  0  as  a  center 
and  a  radius,  Ob,  equal,  on  any  desired  scale,  to  the 
steam  lap,  draw  the  steam  lap  circle  cutting  OB  and 
OC  at  b  and  c,  respectively.  Now  pass  a  circle 
through  the  points  c,  O,  and  b,  and  it  will  be  the 
required  valve  circle.  The  center  of  the  valve  circle  may 
be  found  by  the  ordinary  method  of  finding  the  center  of 
a  circle  that  shall  pass  through  three  given  points ;  or,  if 


104  STEAM    ENGINES    AND    BOILERS. 

desired,  the  diameter  Om  of  the  required  circle  may  be 
obtained  by  drawing,  at  c,  the  line  cm  perpendicular  to 
OC  and  continuing  it  until  it  meets,  at  m,  the  line  bm 
drawn  perpendicular  to  Ob  at  by  and  then  connecting  the 
points  O  and  m. 

The  center  of  the  eccentric  is  at  m  when  the  crank  is 
on  the  dead  center;  the  angle  YOm  is  the  angle  of 
advance  ;  the  line  Om  is  the  required  eccentricity,  equal 
to  half  the  travel  of  the  valve ;  and  da  is  the  required 
lead. 

Problem  j.  Given  the  point  of  admission,  the  point  of 
cut-off,  and  the  lead ;  find  the  angle  of  advance,  the  eccen- 
tricity',  and  the  steam  lap. 

As  explained  in  Problem  i,  the  diameter  of  the  valve 
circle  always  bisects  the  angle  between  the  positions  of 
the  imaginary  crank  at  admission  and  at  cut-off.  From 
Fig.  42,  we  see  that  the  lead,  da,  is  equal  to  Oa  —  Od; 
and,  since  Od  is  equal  to  Ob,  we  have  da  =  Oa  —  Ob. 
But  from  the  triangle  Oma,  we  have  Oa  =±=  Om  cos.  mOa; 
and  from  the  triangle  Omb,  we  have  Ob  =  Om  cos.  mOb. 
Therefore,  da  =  Oa —  Ob  =  Om  \cos.  mOa  —  cos.  mOb~\. 

Since  the  angles  mOa  and  mOb  are  constant  for  a  given 
admission  and  cut-off,  it  follows  that  da  will  vary  directly 
as  Om.  Therefore,  to  solve  the  problem  proceed  as 
follows :  — 

In  Fig.  43,  let  AA\  be  the  stroke  of  the  engine ;  A  C A\  B, 
the  crank  circle;  OB  and  OC,  the  positions  of  the  imag- 
inary crank,  obtained  as  in  the  preceding  problems,  at 
admission  and  cut-off,  respectively.  Bisect  the  angle 
COB  by  the  line  Om,  and  the  angle  YOm  will  be  the 
angle  of  advance. 

On  the  line  Om  take  any  point,  such  as  m,  and  from  it 
draw  md  perpendicular  to  O  B,  and  ma  perpendicular  to 
OA.  With  O  as  a  center  and  a  radius  Od,  draw  an  arc 
cutting  OAi  at  e.  ea  would  be  the  lead  for  an  eccentricity 
equal  to  Om.  As  has  been  shown,  the  lead  is  directly 


VALVE    DIAGRAMS. 


105 


proportional  to  the  eccentricity,  and  the  given  lead  is  to 
ea  as  the  required  eccentricity  is  to  Om.  Therefore, 
make  Of  equal  to  ea,  and  Og  equal  to  the  given  lead. 
Connect  the  points  /  and  m,  then,  through  gt  draw  gn 
parallel  to  fm  and  intersecting  Om  in  the  point  n. 
On  is  the  required  eccentricity. 

Draw,  through  n,  the  line  ndi  parallel  to  md  and  inter- 
secting OB  at  d\,  Odi  will  be  the  required  steam  lap. 

Y 

C 


Fig.  43. 

Having  found  the  angle  of  advance  and  the  eccentric- 
ity, the  valve  circle  may  be  drawn  if  desired. 

Problem  4..  Given  the  point  of  cut-off,  the  lead,  and  the 
maximum  opening  of  the  port ;  find  the  angle  of  advance, 
the  eccentricity,  and  the  steam  lap. 

This  problem  is  met  with  in  steam  engine  designing 
more  than  perhaps  any  other  relating  to  the  valve, 
and  it  is  probably  the  most  difficult  to  solve  exactly. 
It  is  usually  solved  by  trial  and  approximation.  The 
exact  solution  is  usually  difficult  for  the  student,  because 
the  reasons  for  the  different  steps  in  the  construction  of 
the  diagram  are  seldom  fully  understood.  In  order  to 


106 


STEAM    ENGINES    AND    BOILERS. 


explain  thoroughly  the  principles  involved,  let  us  suppose 
that  in  Fig.  44  the  problem  has  been  solved,  and  let  us 
determine  the  relations  that  exist  between  the  different 
parts  of  the  diagram.  In  the  diagram,  Orn  is  the  eccen- 
tricity ;  Obt  the  steam  lap ;  ba,  the  lead  ;  and  dm,  the 
maximum  opening  of  the  steam  port.  AI  C\  is  the  dis- 
tance from  the  beginning  of  the  stroke  to  the  point  of 


Fig.  44. 

cut-off,  and  OC  is  the  position  of  the  imaginary  crank  at 
cut-off.  Draw  am,  and,  since  the  arc  Oam  is  a  semi- 
circle, am  will  be  perpendicular  to  OA.  Also  draw  cm, 
and,  since  Ocm  is  a  semi  circle,  it  will  be  perpendicular 
to  OC.  Draw  bh  at  right  angles  to  OA  ;  it  will  intersect 
cm  at  n.  Through  ;«,  draw  hm  parallel  to  OA  and  inter- 


VALVE    DIAGRAMS.  107 

secting  bh  at  h.  km  will  be  equal  to  ba,  the  lead.  Now, 
with  0  as  a  center  and  a  radius  equal  to  Om,  draw  the 
arc  mk  intersecting  OA  at  k;  then  draw  kg  at  right  angles 
to  OA  and  intersecting  hm  at  g.  kg  will  be  equal  to  bk, 
equal  to  dm,  the  maximum  opening  of  the  steam  port. 
Now,  since  Oc  is  equal  to  Ob,  and  the  angles  ncO  and 
nbO  are  right  angles,  if  we  draw  the  line  On  it  will  bisect 
the  angle,  cnb,  between  the  line  nb,  at  right  angles  to  the 
imaginary  crank  on  dead  center,  and  the  line  cm,  at  right 
angles  to  the  imaginary  crank  at  cut-off. 

Continue  On  until  it  cuts  gk  at  /,  and  then  draw  Im. 
Draw  ns  parallel  to  hg  and  intersecting  kl  at  s.  With  n 
as  a  center  and  a  radius  equal  to  ns,  draw  an  arc  cutting 
Im  at  r.  Draw  nr,  and  it  will  be  parallel  to  Om,  as  may 
be  proved  as  follows  :  — 

In   the    two   similar  triangles  Ins  and  10k,    we    have 

-— -  —  —  —  -_ —     But  In  and  /zrare  sides  of  the  triangle 

Inr-,  also  10  and  Om  are  sides  of  the  triangle  10m. 
Therefore,  since  the  triangles  Inr  and  Olm  have  their 
sides  proportional  and  the  angle  nlm  common  to  both, 
they  must  be  similar;  and  the  line  nris  parallel  to  Om. 

In  the  same  way  it  can  be  shown  that  if  the  lines  rs  and 
mk  be  drawn  they  will  be  parallel. 

Knowing  the  relations  that  have  been  shown  to  exist 
between  the  various  parts  of  the  diagram,  the  solution  of 
the  problem  becomes  as  follows  : — 

Let  AA\,  in  Fig.  45,  represent  the  stroke  of  the  engine, 
drawn  to  any  scale,  and  ACA\,  the  crank  circle; 
A\  C\,  the  distance  the  piston  is  from  the  beginning  of 
its  stroke  at  the  point  of  cut-off;  and  OC,  the  position  of 
the  imaginary  crank  at  cut-off. 

Make  Od,  according  to  any  desired  scale,  equal  to  the 
given  lead ;  and  Oa,  equal  to  the  given  maximum  opening 
of  the  steam  port. 

Through  (9  and  a,  respectively,  draw  Ob  and  ^/perpen- 
dicular to  OA.  Through  d,  draw  cd  at  right  angles  to 


108 


STEAM    ENGINES    AND    BOILERS. 


OC.  Bisect  the  angle  ceb  by  the  line  O'e,  and  prolong  it 
until  it  intersects  af  at  /.*  Connect  /  and  d  by  the  line 
fd;  and  draw  eg  parallel  to  OA  and  intersecting  fa  at  g. 
With  e  as  a  center  and  a  radius  eg,  draw  the  arc  £•/*  cut- 
ting df 'at  ^5.  Connect  the  points  *  and  h,  and  then  draw 
*/0'  parallel  to  eh  and  intersecting  <9'/at  0'. 


Fig.  45. 

The  angle  Oeh  is  the  required  angle  of  advance  ;  and 
O'd  is  the  required  eccentricity.  Draw  O'b  parallel  to 
OA  and  intersecting  Oe  at  b.  O'b  is  the  steam  lap. 

A  line  through  d  parallel  to  a  line  through  h  and  g  will 
pass  through  the  intersection  of  fa  and  Ob  prolonged. 

*  Thereat  of  the  solution  is  simply  the  solution  of  the  well-known  geo- 
metrical problem  :  Given  two  lines  and  a  point,  to  find  a  point  on  one  of  the  lines 
which  is  equally  distant  from  the  other  line  and  the  given  point,  fe  and/a  are  the 
given  lines  and  d  is  the  given  point  O',  the  required  point  on  fe,  is  equally 
distant  from  d  and  the  line/a  prolonged. 


VALVE    DIAGRAMS. 


109 


Problem  5.  Given  the  angle  of  advance,  the  eccentricity, 
and  the  point  of  compression  ;  find  the  exhaust  lap  and  the 
point  of  release. 

In  Fig.  46,  let  AA\  be  the  stroke  of  the  engine,  drawn 
to  any  desired  scale,  and  the  circle  ABAi,  the  crank 
circle.  Draw  the  line  OB,  making  the  angle  YOB  equal 
to  the  given  angle  of  advance.  Lay  off  AD\  equal  to  the 
distance  of  the  point  of  compression  from  the  beginning 
of  the  return  stroke,  and,  then,  draw  D±  D  at  right 
angles  to  AA\.  Connect  0  and  Z>,  and  OD  will  be  the 
position  of  the  imaginary  crank  at  the  beginning  of  com- 
pression. 


Fig.  46. 

Continue  OB  to  /#,  so  that  Om  is  equal  to  the  given 
eccentricity,  and  on  Om  as  a  diameter  draw  the  valve 
circle  Ocmd,  intersecting  the  line  OD  at  d.  Od  is  the 
required  exhaust  lap. 

With  0  as  a  center  and  a  radius  equal  to  Od,  draw  an 
arc  cutting  the  valve  circle  at  c.  Through  c,  draw  the 
line  OCy  and  it  will  represent  the  position  of  the  imaginary 
crank  when  release  takes  place.  Draw  CCi  perpendicular 


110  STEAM   ENGINES    AND    BOILERS. 

to  AAi,  and   A\C\  will  be  the   distance  of  the   point  of 
release  from  the  beginning  of  the  stroke. 

Problem  6.  Given  the  point  of  compression,  the  point  of 
release,  and  the  eccentricity  ;  find  the  angle  of  'advance and 
the  exhaust  lap. 

An  inspection  of  Fig.  46  will  show  that  the  line  Om 
bisects  the  angle  COD,  which  is  formed  by  the  lines 
indicating  the  positions  of  the  imaginary  crank  at  release 
and  at  compression.  Hence  the  construction  for  the 
solution  of  the  problem  is  as  follows  :  — 

In  Fig.  46,  let  AA\  be  the  stroke  of  the  engine,  and  let 
the  circle  ACAi  be  the  crank  circle.  Let  OC  be  the 
position  of  the  imaginary  crank  at  release,  and  OD  its 
position  at  the  beginning  of  compression.  Draw  OB  bi- 
secting the  angle  COD,  and  on  it  make  Om  equal  to  the 
given  eccentricity.  On  Om,  as  a  diameter,  draw  the 
valve  circle  cutting  OC  at  c,  and  OD  at  d. 

The  angle  YOB  is  the  required  angle  of  advance,  and 
Oc,  equal  to  Od,  is  the  required  exhaust  lap. 

47.  EFFECT  OF  THE  OBLIQUITY  OF  THE  CONNECTING 
ROD  ON  THE  POINT  OF  CUT-OFF.  —  In  Fig.  47,  let  A\  A2 
represent  the  stroke  of  an  engine;  O,  the  center  of  the 
crank  shaft ;  OA-,  the  crank ;  and  AA\,  the  length  of  the 
connecting  rod.  Suppose  the  crank  to  revolve  as  indi- 
cated by  the  arrow. 

Make  Ab  equal  to  A\B\,  and  draw  bB'  perpendicular  to 
AA'  and  cutting  the  crank  circle  at  B '.  If  the  obliquity 
of  the  connecting  rod  were  neglected,  the  crank  would  be 
in  the  position  OB'  when  the  piston  has  moved  through 
the  distance  A\B\  on  its  forward  stroke.  With  B\  as  a 
center  and  a  radius  equal  to  AA\,  describe  an  arc  cutting 
the  crank  circle  at  B.  OB  will  be  the  actual  position  of 
the  crank  when  the  piston  has  gotten  to  B\.  It  makes  no 
difference  where  B\  is  taken ;  the  construction  will  always 
show  that,  on  the  forward  stroke  of  the  engine,  the  obli- 


VALVE    DIAGRAMS. 


Ill 


quity  of  the  connecting  rod  makes  the  actual  position  of 
the  crank  lag  behind  the  position  it  would  occupy  if  there 
were  no  obliquity:  that  is,  in  order  that  the  crank  shall 
turn  through  a  given  angle  A  OB',  the  piston  must  move 


through  a  greater  distance  than  the  distance,  Ab,  that  it 
would  move  through  if  there  were  no  obliquity.  It  fol- 
lows, therefore,  that  on  the  forward  stroke  the  actual  dis- 


112  STEAM    ENGINES    AND    BOILERS. 

tance  of  the  piston  from  the  beginning  of  the  stroke  at 
the  point  of  cut-off  is  greater  than  indicated  by  the  valve 
diagram,  by  an  amount  depending  upon  the  obliquity  of 
the  connecting  rod.  In  other  words,  the  obliquity  of  the 
connecting  rod  makes  the  cut-off  occur  later,  on  the  for- 
ward stroke,  than  indicated  by  the  valve  diagram. 

Let  C\  be  any  position  of  the  piston  on  the  return 
stroke.  Make  cA'  equal  to  C\  Azt  and  draw  cO  perpen- 
dicular to  AA'  and  intersecting  the  crank  circle  at  O. 
OO  would  be  the  position  of  the  crank,  when  the  piston 
is  at  C\  on  the  return  stroke,  if  there  were  no  obliquity  to 
the  connecting  rod.  With  C\  as  a  center  and  a  radius 
equal  to  AAi  draw  an  arc  cutting  the  crank  circle  at  C. 
OC  will  be  the  actual  position  of  the  crank  when  the  piston 
is  at  C\  on  the  return  stroke.  The  construction  shows 
that,  for  a  given  movement  of  the  piston  on  the  return 
stroke,  the  obliquity  of  the  connecting  rod  makes  the 
crank  keep  in  advance  of  the  position  it  would  be  in  if 
there  were  no  obliquity ;  that  is,  in  order  that  the  crank 
shall  turn  through  a  given  angle  A' OC,  the  piston  must 
move  through  a  less  distance  than  the  distance,  A'c,  that 
it  would  move  through  if  there  were  no  obliquity.  It 
follows,  then,  that,  on  the  return  stroke,  the  actual  distance 
of  the  piston  from  the  beginning  of  its  stroke  at  the  point 
of  cut-off  is  less  than  indicated  by  the  valve  diagram,  by 
an  amount  depending  upon  the  obliquity  of  the  connect- 
ing rod.  In  other  words,  the  obliquity  of  the  connecting 
rod  makes  the  cut-off  occur  earlier,  on  the  return  stroke, 
than  indicated  by  the  valve  diagram. 

From  what  has  been  said,  it  is  evident  that  if  the  steam 
laps  of  a  valve  be  made  as  determined  by  the  valve  dia- 
gram, and  the  valve  be  set  with  equal  lead  on  the  head 
end  and  crank  end  of  the  cylinder,  the  point  of  cut-off  will 
occur  earlier  on  the  return  stroke  than  on  the  forward  stroke, 
unless  there  is  some  special  means  of  equalizing  the  points 
of  cut-off.  The  usual  manner  of  equalizing  the  points 


VALVE    DIAGRAMS.  113 

of  cut-off  is  to  set  the  valve  with  a  somewhat  greater 
lead  on  the  head  end  of  the  cylinder  than  on  the  crank 
end.  The  exact  amount  that  the  lead  on  the  head  end 
ought  to  be  made  greater  than  that  on  the  crank  end, 
depends  upon  the  obliquity  of  the  connecting  rod,  the 
eccentricity  of  the  eccentric,  and  the  lead  on  the  crank 
end.  It  may  be  determined  by  making  a  valve  diagram 
for  each  end  of  the  cylinder,  and  using  in  each  diagram 
the  positions  of  the  imaginary  crank  as  determined  by 
taking  into  account  the  obliquity  of  the  connecting  rod. 

48.  SWINGING  ECCENTRICS.  —  Automatic  high  speed 
engines  regulate  by  changing  the  angle  of  advance  or  the 
eccentricity  of  the  eccentric,  or  both,  and  thus  change  the 
point  of  cut-off.  As  no  changes  in  the  angle  of  advance  or 
the  eccentricity  can  affect  the  dimensions  of  the  valve,  the 
steam  lap  and  the  exhaust  lap  must  always  remain  the 
same  for  the  same  valve. 

In  order  to  understand  how  the  cut-off  and  lead  will 
be  affected  by  a  change  in  the  eccentricity  and  angle  of 
advance,  for  a  given  eccentric  and  a  given  valve,  let  us 
refer  to  the  valve  diagram  in  Fig.  48.  There,  ABA\  is 
the  crank  circle ;  OB  is  the  position  of  the  imaginary 
crank  at  cut-off;  OC  is  the  position  of  the  imaginary 
crank  at  admission  ;  YOm  is  the  angle  of  advance  ;  Om 
is  the  eccentricity ;  and  Ob,  equal  to  Oc,  is  the  constant 
steam  lap.  m  is  the  position  of  the  center  of  the  eccen- 
tric when  the  real  crank  is  on  the  dead  center ;  and  ad  is 
the  lead.  The  line  md  is  perpendicular  to  Od,  since  the 
angle  Odm  is  inscribed  in  a  semi-circle. 

Now,  suppose  the  center  of  the  eccentric  to  be  shifted 
to  mi  from  m;  then  the  angle  of  advance  will  be  YOrni, 
and  the  eccentricity  will  be  Om\.  By  the  change  we 
have  decreased  the  angle  of  advance  and  increased  the 
eccentricity.  The  new  valve  circle,  drawn  on  Om\  as  a 
diameter,  intersects  the  lap  circle  at  the  points  b\  and  c\; 

8 


114 


STEAM    ENGINES    AND    BOILERS. 


OB\  is  the  new  position  of  the  imaginary  crank  at  cut-off; 
and  OC\  is  the  new  position  of  the  imaginary  crank  at 
admission. 

By  making,  then,  the  angle  of  advance  less  and  the 
eccentricity  greater,  we  have  made  the  cut-off  occur 
later.  If  we  should  consider  m1  the  original  position  of 


the  center  of  the  eccentric  and  m  its  final  position,  we 
see  that  by  increasing  the  angle  of  advance  and  decreas- 
ing the  eccentricity,  we  make  the  cut-off  occur  earlier. 
We  obtain,  therefore,  the  following  propositions:  — 


VALVE    DIAGRAMS.  115 

1.  To  make  the  cut-off  occur  later,  make  the  angle  of 
advance  less  and  the  eccentricity  greater. 

2.  To  make  the  cut-off  occur  earlier,  make  the  angle  of 
advance  greater  and  the  eccentricity  less. 

It  now  remains  to  see  what  effect  is  produced  on  the 
lead  by  changing  the  angle  of  advance  and  the  eccen- 
tricity. In  Fig.  48  it  is  seen  that  changing  the  center  of 
the  eccentric  from  m  to  m±  has  changed  the  lead  from  ad 
to  ad\.  Draw  m\d\  and,  since  the  angle  Od\m\  is  inscribed 
in  a  semi-circle,  it  will  be  perpendicular  to  OA\.  Since 
adi  is  greater  than  ad,  the  line  m\d±  lies  to  the  right  of  md. 
Therefore,  it  is  seen  that  if,  when  the  cut-off  is  changed,  the 
lead  becomes  greater,  the  center  of  the  eccentric  will  lie  to 
the  right  of  a  line  drawn  through  its  original  position  per- 
pendicular to  the  center  line  of  the  engine. 

If  the  lead  had  remained  constant,  ad\  would  be  equal 
to  ad  and  the  line  m\d\  would  coincide  with  md.  There- 
fore, it  follows  that,  if  the  lead  remains  constant  when  the 
cut-off  is  changed,  the  center  of  the  eccentric  will  remain  on 
a  line  drawn  through  its  original  position  perpendicular  to 
the  center  line  of  the  engine. 

If  ad\  were  less  than  ad,  the  lead  would  be  less  than 
before  and  the  line  m±d±  would  lie  to  the  left  of  md.  That 
is,  if  the  lead  is  decreased  when  the  cut-off  is  changed,  the 
center  of  the  eccentric  will  lie  to  the  left  of  a  line  drawn 
through  its  original  position  perpendicular  to  the  center  line 
of  the  engine. 

Very  few  engines  preserve  a  constant  lead  under  vary- 
ing cut-offs,  owing  to  the  difficulty  of  making  the  center 
of  the  eccentric  have  a  straight-line  motion,  as  it  must  in 
order  that  m\  may  always  fall  on  md. 

On  most  engines  of  the  automatic  high  speed  type 
the  eccentric  is  swung  about  a  pin  outside  the  shaft,  so 
that,  as  the  angle  of  advance  is  changed,  the  center,  m,  of 
the  eccentric  moves  in  the  arc  of  a  circle  whose  center  is 
the  center  of  this  suspending  pin.  Making  the  eccentric 


116  STEAM    ENGINES    AND    BOILERS. 

swing  about  the  pin  effects  a  continual  variation  in  the 
lead,  as  the  point  of  cut-off  is  changed,  and  the  way  in 
which  the  lead  varies  depends  upon  the  relative  positions 
of  the  center  of  the  suspending  pin,  the  center  of  the 
shaft,  and  the  center  of  the  eccentric.  Usually, 
although  not  always,  the  lead  is  made  to  decrease  as  the 
cut-off  becomes  later.  Often,  the  lead  is  made  zero  for 
cut-off  at  one-quarter  stroke,  negative  for  points  of  cut- 
off later  than  one-quarter,  and  positive  for  points  of  cut-off 
earlier  than  one-quarter.  In  such  cases,  the  center  of  the 
shaft  is  between  the  center  of  the  suspending  pin  and 
the  center  of  the  eccentric. 

The  position  of  the  center  of  the  suspending  pin  is 
found  by  assuming  three  required  positions  of  the  center 
of  the  eccentric,  and  finding  the  center  of  a  circle  that  will 
pass  through  these  positions.  The  center  of  this  circle 
will  be  the  required  center  of  the  suspending  pin. 

In  Fig.  49  is  shown  a  diagram  of  a  governor  similiar 
to  that  used  on  the  Straight  Line  engine.  R  is  the  eccen- 
tric, which,  as  shown,  is  carried  by  the  frame  Tt  and 
which  has  an  opening  in  it  through  which  the  shaft  passes. 
The  eccentric  and  frame  swing  about  the  pin  S,  on  the 
governor  wheel.  When  the  engine  is  cutting  off  at  its 
latest,  the  center  of  the  eccentric  is  at  n;  and  when  the 
engine  is  cutting  off  at  its  earliest,  the  center  of  the  eccen- 
tric is  at  a.  The  center  of  the  eccentric  is  shown  in  Fig. 
49  as  at  n,  and  the  eccentricity  is  the  distance  of  n  from 
the  center  of  the  shaft.  When  the  engine  is  run,  the 
centrifugal  force  of  the  weight  C  tends  to  make  it  move 
farther  from  the  center  of  the  shaft.  When  C  moves,  it 
moves  about  the  pin  0,  and,  by  means  of  the  link  //", 
makes  the  frame,  Tt  and  the  eccentric,  R,  move  about  S 
as  a  center ;  so  that  the  center  of  the  eccentric  moves 
from  n  towards  a.  When  C  is  moved  outward  by  its  cen- 
trifugal force  it  will  bend  the  spring  E,  to  which  it  is  con- 
nected by  the  band  P,  until  the  resistance  to  bending  of 
E  is  equal  to  the  moving  force  acting  on  C ;  then  the 


VALVE    DIAGRAMS.  117 

eccentric  will  be  at  rest,  with  its  center  somewhere  between 
n  and  a. 

If,  on  account  of  an  increased  load,  the  speed  of  the 
engine  should  be  decreased,  the  centrifugal  force  of  C 
would  become  smaller,  and  the  spring  would  pull  C 
towards  the  center  of  the  shaft,  and  move  the  center 
of  the  eccentric  towards  n;  thus,  the  cut-off  would 


Fig.  49. 

be  made  later  and  an  increased  amount  of  steam  would 
be  admitted  into  the  engine  to  make  it  go  faster.  So, 
also,  if,  on  account  of  a  decrease  in  the  load,  the  speed  of 
the  engine  should  increase,  the  centrifugal  force  would 
become  greater,  and  C  would  move  farther  from  the  center 
of  the  shaft,  thus  moving  the  center  of  the  eccentric 
toward  a,  making  the  cut-off  earlier,  and  reducing  the 
amount  of  steam  admitted  to  the  engine. 


CHAPTER     VI. 

INDICATORS    AND    INDICATOR  CARDS. 

49.  INDICATORS. —  The  indicator  is  an  instrument  by 
means  of  which  the  actual  work  diagram  of  the  steam  in 
the  cylinder  of  an  engine  is  automatically  drawn  on  a 
piece  of  paper.  The  diagram  obtained  by  the  use  of  the 
indicator  is  termed  an  "  indicator  card." 

There  are  several  indicators,  which  differ  from  one 
another  in  their  details  only,  for  sale  on  the  market. 

In  Fig.  50  is  shown  a  view  of  the  Crosby  indicator, 
made  by  the  Crosby  Steam  Gauge  &  Valve  Co.,  Boston, 
Mass.  It  consists  of  the  "  drum  "  A,  on  which  the  paper 
for  the  card  is  held  by  clips  a  ;  the  cylinder  Ft  in  which 
works  a  steam  tight  piston  connected  to  the  piston,  rod 
G ;  and  a  lever  Kt  which  carries  a  pencil  c,  at  its  free 
extremity.  The  motion  of  the  engine  is  reduced  by  a 
suitable  reducing  motion  and,  by  means  of  a  cord  D,is  com- 
municated to  the  drum  A.  As  the  piston  moves  forward, 
the  drum  is  turned  in  one  direction  by  the  pull  on  Dy 
and  as  it  moves  back,  on  its  return  stroke,  the  drum  is 
turned  in  the  opposite  direction  by  means  of  a  strong 
spring  inside  of  it,  which  is  shown  in  the  sectional  view 
of  the  indicator  given  in  Fig.  51.  It  is  evident  that  if, 
during  the  backward  and  forward  motion  of  the  drum, 
the  pencil  c  had  been  kept  at  rest  and  pressed  against  the 
paper,  it  would  have  marked  on  there  a  line,  parallel  to 
the  base  of  the  drum,  whose  length  would  be  propor- 
tional to  the  stroke  of  the  engine. 

The  steam  enters  the  cylinder  F,  and  presses  against 
the  piston  and  makes  it  rise  ;  and  it,  in  turn,  makes  the 
pencil  c  rise.  As  seen  in  Fig.  51,  the  piston  in  the  cyl- 
(118) 


INDICATORS    AND    INDICATOR    CARDS. 


119 


inder  is  kept  down  by  a  spring  that  must  be  compressed 
before  the  piston  can  rise.  The  springs  used  to  keep  the 
piston  down  are  numbered  and  named  according  to  the 
number  of  pounds  pressure  per  square  inch  required  to 
raise  the  pencil  c  through  one  inch  :  thus,  a  No.  40 
spring,  or  a  40  Ib.  spring,  is  a  spring  that,  when  in  the 
indicator,  will  require  an  effective  pressure  of  40  Ibs.  per 
square  inch  to  make  c  rise  one  inch. 


Fig.  50. 

By  means  of  the  system  of  levers,  shown  in  Fig.  50,  con- 
necting Kto  the  frame  of  the  indicator  and  to  the  piston 
rod  G,  the  pencil  c  is  made  to  move  in  a  straight  line 
parallel  to  the  axis  of  the  drum  A.  It  is  in  the  system 
of  levers  for  making  c  move  in  a  straight  line,  that  indi- 
cators on  the  market  differ  most. 

The  handle  E  can  be  so  adjusted  by  turning  it  to  the 
right  or  left,  that  when  it  is  pressed  forward,  so  that  its 
inner  end  strikes  against  the  stop  B,  the  pencil  c  will 


120 


STEAM    ENGINES    AND    BOILERS. 


press  with  any  desired  pressure  against  the  paper  on  the 
drum  A.  When  the  pencil  is  pressed  against  the  paper 
it  makes  a  line,  every  point  of  which  represents,  at  once, 
the  position  of  the  piston  in  its  stroke  and  the  pressure 
of  the  steam  at  the  same  instant.  The  position  of  the 
piston  is  indicated  by  the  distance  of  the  point  from  the 
ends  of  the  card;  and  the  pressure  of  the  steam  is 
referred  to  the  "atmospheric  line,"  obtained  by  shutting 
off  the  cylinder  of  the  indicator  from  the  cylinder  of  the 
engine,  putting  it  in  communication  with  the  air,  and 
then  pressing  the  pencil  against  the  paper. 


Fig.  51. 

50.  ADJUSTMENTS  AND  CONNECTIONS  OF  INDICATORS. — 
In  order  that  the  results  obtained  by  the  use  of  an  indi- 
cator may  be  of  value,  it  is  necessary  that  the  various 
parts  should  be  in  adjustment  and  act  as  they  are  designed 
to  act.  If  an  indicator  is  tested,  and  it  is  in  adjustment, 
it  will  be  found  that  :  — 

I.  The    pencil  will  move  in  a  straight  line  parallel  to 


INDICATORS    AND    INDICATOR    CARDS.  121 

the  axis  of  the  drum ;  and  the  line  obtained  by  moving 
the  pencil  and  keeping  the  drum  at  rest,will  be  at  right 
angles  to  the  line  obtained  by  keeping  the  pencil  at  rest 
and  moving  the  drum. 

2.  For  equal  amounts  of  increase  in  the  pressure  on  the 
piston,  the  pencil  will  rise  equal  distances. 

The  motion  of  the  pencil  must  be  adjusted  by  the 
maker  of  the  instrument;  and  if  it  is  not  correct  the  in- 
strument should  not  be  used  for  important  work,  as  the 
cards  obtained  from  it  would  be  distorted,  and  would  be 
apt  to  give  a  wrong  impression  of  the  real  action  of  the 
steam  in  the  cylinder  of  the  engine. 

The  springs  used  in  the  cylinder  of  the  indicator  should 
always  be  tested  hot,  so  that,  when  being  tested,  they  will 
be  as  nearly  as  possible  in  the  same  condition  as  when  in 
actual  use.  It  is  not  necessary  that  the  springs  should  be 
exact,  provided  the  error  is  constant,  and  can  be  deter- 
mined. 

It  is  important  that  the  friction  of  the  pencil  be  as 
little  as  possible  and  that  the  play,  or  back  lash,  in  the 
joints  of  the  levers,  for  producing  the  straight  line  motion 
of  the  pencil,  should  be  as  small  as  possible.  The  fric- 
tion of  the  pencil  on  the  paper  must  be  reduced  to  the 
minimum,  by  adjusting  the  pencil  so  that  it  presses  against 
the  paper  with  sufficient  force  to  just  make  a  mark  and 
no  more. 

The  piston  of  the  indicator  should  be  a  nice  fit  in  the 
cylinder,  and  it  is  preferable  to  have  it  too  loose  rather 
than  too  tight.  The  fit  will  be  about  right  if  the  piston 
will  be  moved  down  the  cylinder  by  its  own  weight,  when 
the  spring  is  removed.  The  piston,  and  all  the  moving 
parts  attached  to  it,  should  be  as  light  as  is  consistent  with 
strength. 

The  drum  of  the  indicator  should  be  light  and  should 
move  easily  on  its  axis.  Its  cross-section  should  be  a  per- 
fect circle  ;  and  its  axis  of  rotation  should  coincide  with 


122  STEAM    ENGINES    AND    BOILERS. 

the  axis  of  the  cylinder.  The  tension  of  the  spring  in  the 
drum  should  be  regulated  so  that  the  inertia  of  the  drum 
will  not  lengthen  the  cards  too  much  ;  it  should  be  greater 
for  high  speed,  than  for  low  speed  engines. 

The  indicator  is  connected  to  the  cylinder  of  the  engine 
by  a  piece  of  half-inch  pipe;  and,  while  much  differ- 
ence of  opinion  seems  to  exist  as  to  whether  or  not  the  card 
obtained  with  a  short  connection,  having  as  few  bends  as 
possible,  is  materially  different  from  that  obtained  with  a 
long  connection,  having  several  bends,  it  is,  undoubtedly, 
true  that  the  long  connections  do  no  good  ;  and,  there- 
fore, the  connections  should  be  as  short  as  possible. 
Where  the  load  on  an  engine  fluctuates  through  wide 
ranges,  it  is  almost  impossible  to  determine  with  any 
degree  of  accuracy,  from  the  cards  of  an  engine,  whether 
or  not  the  valves  are  properly  adjusted,  unless  cards  are 
taken  at  the  same  time  from  both  ends  of  the  engine. 
To  do  this,  it  is  necessary  to  have  two  indicators,  one  at 
each  end  of  the  cylinder  ;  they  should  be  so  arranged 
that  when  the  pencil  of  the  one  is  pressed  against  its 
paper,  the  pencil  of  the  other  will,  also,  be  pressed  against 
its  paper.  Where  two  indicators  cannot  be  arranged  to 
work  together,  so  that  cards  may  be  taken  simultaneously 
from  each  end  of  the  cylinder,  and  a  single  indicator  is 
used,  it  should  be  connected  to  the  ends  of  the  cylinder 
so  that  it  will  not  be  necessary  to  change  its  position  in 
order  to  take  a  card  from  either  end  of  the  cylinder. 
The  best  method  of  making  the  connections  for  a  single 
indicator  is  to  connect  both  ends  of  the  cylinder  to  a 
single  pipe,  along  the  side  of  the  cylinder,  and  in  the 
middle  of  this  pipe  put  a  three-way  cock,  to  which  the 
indicator  may  be  attached.  Makers  of  indicators  make 
special  three-way  cocks  for  indicator  connections. 

51.  REDUCING  MOTIONS. —  As  the  diameters  of  the 
drums  of  indicators  are,  usually,  either  ij  or  2  inches, 


INDICATORS    AND    INDICATOR    CARDS.  123 

their  circumferences  will  be  about  5  or  6  inches  ;  and,  as 
the  length  of  the  card  taken  on  an  indicator  must  be 
considerably  shorter  than  the  circumference  of  the  drum, 
the  cards  will  usually  be  3  inches  long  for  a  drum  ij 
inches  in  diameter,  and  about  4  inches  long  for  a  drum  2 
inches  in  diameter.  The  drum  is  connected  to  some 
point  on  the  engine  that,  by  a  suitable  "  reducing 
motion,"  makes  the  drum  move  through  a  distance  equal 
to  the  desired  length  of  the  indicator  card.  The  motion 
of  this  point  must  be  such  that  the  drum  of  the  indicator 
will  make  one  complete  movement  in  one  direction,  dur- 
ing the  same  time  that  the  engine  makes  one  stroke  ;  also, 
the  ratio  of  the  velocity  of  turning  of  the  drum,  at  any 
instant,  to  the  velocity  of  the  piston,  at  the  same  instant, 
ought  to  be  a  constant  quantity.  If  this  last  requirement 
is  not  fulfilled,  the  card  will  be  distorted,  shortened  up  at 
some  places  and  lengthened  out  at  others,  so  that  an 
event  which  occurs  at,  say,  one  quarter  of  the  stroke  of 
the  engine,  will  be  shown  on  the  card  as  occurring  either 
before  or  after  one  quarter  stroke.  To  test  the  accuracy 
of  a  reducing  motion,  put  the  engine  on  dead  center,  so 
that  the  piston 'is  just  beginning  its  stroke,  and  mark  the 
position  of  the  pencil  on  the  indicator  card.  Now  divide 
the  distance  through  which  any  chosen  point  on  the  cross- 
head  moves,  during  one  revolution,  into  a  number,  such  as 
four  or  eight,  of  equal  parts,  and  make  a  mark  at  each 
point  of  division.  Move  the  piston  forward  until  the 
chosen  point  on  the  cross-head  coincides  with  the  first 
division  mark,  and  mark  the  position  of  the  pencil  on  the 
drum  ;  then  move  the  cross-head  to  the  next  division 
mark,  and  mark,  again,  the  position  of  the  pencil  on  the 
drum.  Continue  moving  the  cross-head  forward  one 
division,  and  marking  the  corresponding  motion  of  the 
drum,  until  the  piston  has  made  one  stroke.  Take  the 
card  off  the  drum  and  determine  whether  or  not  the  dis- 
tance between  any  two  successive  marks  is  always  the 


124  STEAM   ENGINES   AND    BOILERS. 

same ;  if  it  is,  the  reducing  motion  is  correct,  but  if  it  is 
not,  the  reducing  motion  is  defective. 

The  commonest  form  of  reducing  motion  is  the  "  pen- 
dulum motion,"  shown  in  Fig.  52.  It  consists  of  a  bar, 
A,  slotted  at  one  end,  and  suspended  by  a  pin,  B,  at  the 
other  end.  A  pin,  c,  fastened  to  the  cross-head,  fits  in 
the  slot  at  the  lower  end  of  the  bar  ;  and  a  pin,  D,  is  fast- 
ened to  the  bar.  The  string  from  the  drum  of  the  indi- 
cator is  tied  to  D.  As  the  engine  moves  backward  and 
forward,  the  pin  c  makes  the  bar  oscillate  about  B  as 
a  center.  At  any  instant,  the  ratio  of  the  velocity  of  the 


Fig.  52. 

/?  D 
drum  to  the  velocity  of  the  piston  is  equal  to  ~~n^>  As 

Be  changes  for  different  positions  of  the  piston,  this 
ratio  is  not  a  constant  one.  The  point  D  moves  in  the 
arc  of  a  circle  whose  center  is  B;  and,  therefore,  the 
direction  of  the  string,  leading  from  D  to  the  drum  of  the 
indicator,  is  constantly  changing.  This  makes  a  slight 
error  in  the  motion  of  the  drum.  If  Be  is  not  made  less 
than  twice  the  length  of  the  stroke  of  the  engine  and, 
when  in  mid-position,  is  perpendicular  to  the  direction  of 
the  motion  of  the  piston,  and  the  string  is  lead  off  per- 
pendicular to  Be  in  mid-position,  it  will  be  found  that 
the  errors  of  the  motion  will  be  small,  and  the  motion 
will  give  fairly  good  results. 


INDICATORS    AND    INDICATOR    CARDS.  125 

The  length  of  the  card  given  by  this  motion  is  equal  to 
the  length  of  the  stroke  of  the  engine  multiplied  by  the 
length  of  BD  and  divided  by  the  length  of  Be. 

The  "  Brumbo  Pulley,"  shown  in  Fig.  53,  is  a  motion 
devised  to  overcome  the  errors  of  the  simple  pendulum 
motion.  It  is  more  elaborate  then  the  simple  pendulum 
motion.  It  consists  of  a  link,  A,  which  is  suspended  by 
a  pin,  B,  and  to  which  is  fastened  an  arc,  D,  whose  center 
coincides  with  that  of  the  pin  B.  The  lower  end  of  A  is 
connected  to  the  cross -head,  by  the  link  C.  It  is  usual  to 
make  the  link  A,  when  in  mid-position,  perpendicular  to 
the  line  of  motion  of  the  piston. 


By  assuming  the  length  of  the  links  A  and  C,  and 
plotting  the  required  motion  of  the  drum,  for  given 
motions  of  the  piston,  a  form  of  arc  may  be  obtained  that 
will  give  a  perfectly  correct  motion  to  the  drum  of  the 
indicator.  It  is  usual,  however,  to  make  D  the  arc  of  a 
circle ;  and,  then,  the  motion  is  not  exact,  but  the  error 
due  to  the  obliquity  of  the  string  leading  from  D  is 
avoided,  as  its  direction  is  not  changed. 


126  STEAM    ENGINES    AND    BOILERS. 

In  Fig.  54  is  shown  the  "  pantograph  "  used  on  long 
stroke  engines.  It  gives  a  perfect  motion  if  properly 
used. 

The  instrument  is  made  of  a  number  of  light  wooden 
links  joined  together  as  shown.  When  used,  the  pivot  B 
is  fastened,  by  means  of  the  thumb  screw  on  its  end,  to 
any  convenient  support.  The  pin  A  is  dropped  into  an 
opening  either  in  the  cross-head  itself  or  in  a  piece 
fastened  to  the  cross-head ;  so  that,  while  B  remains 
stationary,  A  has  the  motion  of  the  cross-head.  The 
cord  leading  to  the  indicator  is  fastened  to  a  pin,  E,  in 
the  cross-head  bar  DC,  and  should  be  lead  off  parallel  to 
the  line  of  motion  of  the  piston. 


Fig.  54. 

This  instrument  may  be  used  either  in  a  horizontal  or  a 
vertical  position,  whichever  is  the  more  convenient,  and 
will  give  equally  good  results  in  either  position. 

The  length  of  the  card  depends  upon  the  ratio  of  the 
distance  BE  to  the  distance  BA,  and  upon  the  stroke  of 
the  engine.  For  a  given  position  of  the  cross-bar,  BC, 
and  the  pin,  E,  in  it,  the  ratio  of  BE  to  BA  is  a  constant 
one,  no  matter  how  long  the  instrument  maybe  stretched. 
The  position  of  the  cross-bar,  DC,  may  be  changed  by 
changing  the  holes  in  which  the  pins  D  and  C  are 
placed.  The  bar  DC  must  always  be  parallel  to  the  left- 


INDICATORS    AND    INDICATOR    CARDS.  127 

hand  bar  passing  through  B.  The  pin,  E,  on  the  cross- 
bar, DC,  must  be  placed  so  that  it  is  on  the  line  BA.  The 
joints  of  the  instrument  must  be  kept  tight  and  well 
lubricated. 

The  length  of  the  card  given  by  this  instrument  is 
equal  to  the  length  of  the  stroke  of  the  engine  multiplied 
by  the  length  of  BE  and  divided  by  the  length  of  BA. 

In  Fig.  55  is  shown  one  of  the  many  forms  of  "re- 
ducing wheels/'  used  in  connection  with  high  speed 
engines.  Its  construction  is  evident  from  the  figure. 
The  cord  from  the  large  drum  leads  to  the  cross-head  of 
the  engine,  and  that  from  the  small  drum  leads  to  the 
indicator. 


Fig.  55. 


52.  CORD  FOR  INDICATOR.  —  The  cord  used  for  trans- 
mitting the  motion  of  the  reducing  mechanism  to  the 
drum  of  the  indicator,  should  be  a  good  quality  of  strong, 
cotton,  cord  that  has  but  little  stretch.  Where  the  dis- 
tance from  the  reducing  mechanism  to  the  indicator  is 
great,  it  is  preferable  to  use  good  steel  wire  instead  of 
cord. 


128  STEAM    ENGINES    AND     BOILERS. 

In  leading  off  from  the  reducing  motion,  the  cord  should 
always  run,  for  a  short  distance  at  least,  parallel  to  the 
direction  of  motion  of  the  piston  of  the  engine.  If  this  is 
not  done,  there  will  be  an  error  due  to  the  obliquity  of  the 
cord. 

In  changing  the  direction  of  the  cord  it  should  be 
passed  over  small  guide  pulley-wheels,  made  for  that 
purpose. 

It  is  customary  to  have  a  loop  in  the  end  of  the  lead- 
ing, cord  in  which  may  be  caught  the  hook  that  is  usually 
attached  to  the  end  of  the  cord  fastened  to  the  drum  of  the 
indicator.  By  unfastening  the  hook  from  the  loop,  the 
indicator  will  be  disconnected  from  the  engine  and 
stopped,  and  the  card  on  the  drum  may  be  changed ;  by 
catching  the  hook  in  the  loop,  the  indicator  may  be  put 
in  motion  again. 

53.  TAKING  THE  INDICATOR  CARD. —  To  take  a  card,  turn 
steam  on  the  indicator  and  wait  until  it  has  got  thoroughly 
warm ;  connect  the  drum  to  the  reducing  motion ;  open 
the  communication   between  one  end  of  the  cylinder  of 
the  engine  and  the  cylinder  of  the  indicator ;  press  the 
pencil  against  the    paper,  and    hold    it  there    while   the 
engine  makes  one  revolution  ;   then  shut  off  the  indicator 
from  the  engine,  and  at  once  take  the  atmospheric  line. 
If  the  indicator  is  connected  so  that  a  card  may  be  taken 
from  both  ends  of  the  engine,  take  a  card  from  one  end, 
then,   as  rapidly  as  possible,  shut  off  that  end  and  take 
the  card  from  the   other   end,  before   taking  the  atmos- 
pheric line. 

While  one  man  is  taking  the  indicator  card,  another 
ought  to  be  getting  the  number  of  revolutions  of  the 
engine. 

54.  To  DETERMINE  THE  HORSE-POWER  FROM  THE  INDI- 
CATOR CARD. —  The    indicator    card   gives    us    the    real 


INDICATORS  AND  INDICATOR  CARDS. 


129 


"work  diagram"  of  the  steam  in  the  cylinder,  and,  as 
has  been  explained  in  Article  22,  the  area  of  this  diagram 
represents  the  work  done,  by  the  steam  on  the  engine,  each 
time  steam  enters  the  cylinder.  Therefore,  if  we  get  the 
area  of  the  diagram  in  square  inches  and  divide  it  by  the 
length  of  the  diagram  in  inches,  we  shall  obtain  the  mean 
height  of  the  diagram.  If  this  mean  height  be  multiplied 
by  the  number  of  the  indicator  spring  we  shall  get  the 
mean  effective  pressure,  Pe,  per  square  inch,  of  the  steam 


Fig.  56. 

on  the  piston ;  and  if  we  put  this  value  of  Pe  in  the 
equation  for  the  horse-power  of  an  engine,  as  given  by 
(54)  of  Art.  22,  we  get 

PeL  AN 


H.  P.= 


33000 


As  explained  in  Art.  22,  L  is  the  stroke  of  the  engine 
in  feet ;  A,  the  area  of  the  piston  in  square  inches  ;  and  Nt 
the  number  of  times  per  minute  the  engine  takes  steam. 
If  the  engine  is  double  acting,  N  is  equal  to  the  number 


130  STEAM    ENGINES    AND    BOILERS. 

of  strokes,  or  twice  the  number  of  revolutions  made  per 
minute.  Pe,  for  a  double  acting  engine,  ought  to  be  taken 
as  the  mean  of  the  values  of  Pe  derived  from  the  cards 
from  both  ends  of  the  cylinder. 

The  best  method  of  determining  the  area  of  an  indicator 
card  is  to  use  the  Amsler  Planimeter,  shown  in  Fig.  56. 
The  card  is  fastened  to  a  drawing  board,  or  the  smooth 
top  of  a  table,  and  the  point  A  of  the  instrument  pressed 
into  the  drawing  board  or  table,  so  that  it  cannot  move. 
The  tracing  point,  B,  of  the  instrument  is  now  put  at  any 
convenient  point  on  the  line  of  the  card,  and  the  reading 
of  the  scale  on  the  wheel  C  is  determined  by  means  of 
the  venier  £,  which  enables  one  to  read  to  the  hundredth 
part  of  a  square  inch.  The  tracing  point,  B,  is  now  moved 
around,  always  in  a  right-handed  direction,  on  the  line  of 
the  card  until  it  returns  to  the  point  from  which  it  was 
started.  The  scale  on  the  wheel  is  again  read,  and  the 
difference  between  the  last  reading  and  the  first  reading, 
of  the  scale  en  C,  is  the  area  of  the  diagram  in  square 
inches.  Measure  the  length  of  the  diagram;  then  divide 
the  area  of  the  diagram  by  the  length  of  the  diagram,  and 
the  result  multiplied  by  the  number  of  the  indicator 
spring,  is  the  mean  effective  pressure,  Pe,  to  be  used  in 
calculating  the  horse-power. 

The  price  of  planimeters  is  now  so  small  that  it  is 
rather  unusual  for  any  person  who  has  an  indicator  to  be 
without  a  planimeter,  but  for  the  sake  of  those  who  do 
not  have  one,  the  method  of  obtaining  the  value  of  Pe 
without  the  use  of  the  planimeter  is  given.  In  Fig.  57, 
let  AB  represent  the  atmospheric  line  of  the  card. 
Through  A,  draw  AC  in  any  convenient  direction.  Take 
any  convenient,  small  distance,  AD,  on  AC.  From  D  lay 
off  successively  nine  equal  distances,  DF,  FG,  GH,  etc., 
to  N ;  and  make  each  of  these  distances  equal  to  twice  the 
length  of  AD.  Now  lay  off  NC  equal  to  AD,  and  draw 
BC.  Through  the  points  D,  F,  G,  H,  etc.,  on  AC,  draw 


INDICATORS    AND    INDICATOR    CARDS. 


131 


lines  parallel  to  BC  and  intersecting  AB  at  the  points 
d>f,g,  h,  etc.  Through  the  points  dyf,g,  /z,  etc.,  draw 
lines,  IT,  22,  33,  44.,  etc.,  perpendicular  to  AB  and,  each, 
intersecting  the  bounding  line  of  the  card  in  two  points. 


Get  the  sum  of  the  distances  //,  22,  33,  44.,  etc.,  and 
divide  it  by  ten  ;  multiply  this  quotient  by  the  number  of 
the  indicator  spring,  and  the  result  will  be  the  value  of 
mean  effective  pressure,  Pet  to  be  used  in  determining  the 
horse-power  of  the  engine. 


132 


STEAM    ENGINES    AND    BOILERS. 


55.  To  FIND  THE  RATIO  OF  CLEARANCE  OF  THE  ENGINE 
FROM  THE  INDICATOR  CARD  —  In  Fig.  58  we  have  a  card 
whose  atmospheric  line  is  AB.  That  part  of  the  bound- 
ing line  of  the  card  from  I  to  2  is  made  during  admission 
of  the  steam  to  the  cylinder ;  that  part  from  2  to  3  is 
made  during  expansion  of  the  steam,  after  cut-off  at  2 ; 
that  part  from  4  to  5  *s  made  during  the  return  stroke, 
while  the  exhaust  valve  is  open ;  and  that  part  from  5  to 
6  is  made  during  compression,  after  the  exhaust  valve 


Fig.  58. 

closed  at  5.  The  part  from  3  to  4  is  made  at  the  end  of 
the  stroke,  when  the  pressure  suddenly  falls,  from  the  final 
pressure  of  the  steam  after  expansion,  to  almost  the  atmos- 
pheric pressure ;  and  the  part  from  6  to  I  is  made  when 
the  steam  begins  to  enter  the  cylinder,  just  before  the 
beginning  of  the  forward  stroke. 

To  find  the  ratio  of  the  clearance  volume  to  the  volume 
swept  through  by  the  piston  during  one  stroke,  draw  AA\ 
perpendicular  to  the  atmospheric  line ;  and  lay  off  AAl 
so  that,  according  to  the  scale  of  pressures  of  the  card,  it 
will  be  equal  to  the  atmospheric  pressure,  14.7  Ibs.  per 
square  inch.  Through  A\,  draw  A\B  parallel  to  AB. 


INDICATORS    AND    INDICATOR    CARDS.  133 

Now  take  any  two  points,  such  as  a  and  b,  on  the  com- 
pression line  56.  Through  a  draw  a  line  parallel  to  AB, 
and  continue  it  until  it  intersects,  at  c,  a  line  drawn 
through  b  perpendicular  to  AB;  also,  through  a  draw  a 
line  perpendicular  to  AB,  and  continue  it  until  it  intersects, 
at  </,  a  line  drawn  through  b  parallel  to  AB.  Draw  cd 
and  continue  it  until  it  intersects  A\B\  at  0,  the  "origin  " 
of  the  card. 

Through  O,  draw  OY  perpendicular  to  AB  and  inter- 
secting it  at  e.  Then,  the  ratio  of  Ae  to  AB  will  be  the 
ratio  of  the  volume  of  clearance,  at  that  end  of  the 
cylinder  from  which  the  card  was  taken,  to  the  volume 
swept  through  by  the  piston  in  one  stroke.  This  con- 
struction is  based  upon  the  supposition  that  the  curve 
56  is  an  equilateral  hyperbola.  The  ratio  obtained 
may,  or  may  not,  be  the  same  for  both  ends  of  the 
cylinder. 

56.  To  FIND  THE  WEIGHT  OF  STEAM  USED  PER  HOUR 
PER  HORSE-POWER. —  Take  any  point,/,  near  the  end  of 
the  expansion  line,  and  through  it  draw  the  line  fg 
parallel  to  AB  and  intersecting  the  compression  line  at^. 

Let  the  ratio  obtained  by  dividing  the  length  offg  by 
the  length  of  AB  be  denoted  by  X. 

The  volume  of  the  steam,  at  the  pressure  by  the  gauge 
equal  to  the  pressure  corresponding  to  hft  that  is  used 
per  stroke  is  equal  to  the  volume  swept  through  by  the 
piston,  in  one  stroke,  multiplied  by  X.  Since  the  volume, 
in  cubic  feet,  swept  through  by  the  piston  per  stroke  is 

LA  XLA 

— ,  the  volume  of  steam  used  per  stroke  is . 

144  144 

If  the  number  of  strokes  made  per  minute  is  N,  the 
number  made  per  hour  will  be  60  A7",  and  the  volume  of 
steam,  at  a  gauge  pressure  corresponding  to  hfy  used  per 
hour  will  be 

GO  XL  AN        $  XL  AN 
144  ~12~ 


STEAM    ENGINES    AND    BOILERS. 

Let  s  be  the  volume,  in  cubic  feet,  of  one  pound  of 
steam  at  the  gauge  pressure  corresponding  to  the  pressure 
/{/",  as  obtained  from  Table  I ;  then  the  weight  of  steam 
used  per  hour  by  the  engine  will  be 


s  12  s 

From  (54),  we  have  that  the  horse-power  of  the  engine 
If.  P.  = 


is 

PeL  AN 


53000 

The  weight  of  steam  used  per  hour  per  horse-power 
will  be,  from  (61), 

S        _  165000  X_    13750  X 
H.  P.    :     ~\l~sJ\~  sPe 

X  and  Pe  are  obtained  from  the  indicator  card,  and  s  is 
obtained  from  Table  i. 


57.  INTERPRETATION  OF  THE  ACTION  OF  THE  VALVES 
FROM  THE  APPEARANCE  OF  THE  INDICATOR  CARD. —  In 
studying  the  cards  shown  in  this  article,  the  student  must 
remember  that  each  card  is  drawn  to  illustrate  some 
special  defect,  which  is  made  very  prominent  and  which 
may  be  much  less  prominent  on  a  card  from  an  engine. 

Wire-drawing  or  Throttling  is  indicated  by  the  admis- 
sion line  gradually  dropping,  from  the  beginning  of  the 
stroke  to  the  point  of  cut-off,  below  a  line  drawn  parallel 
to  the  atmospheric  line  through  the  point  indicating  the 
initial  pressure  of  the  steam,  as  shown  at  12  in  Fig.  59. 
Wire-drawing  is  due,  in  the  case  of  non-throttling  engines, 
to  the  valve  not  opening  far  enough  to  admit  the  steam 
to  the  cylinder,  or  to  bad  and  poorly  designed  ports.  In 
the  case  of  throttling  engines,  the  wire-drawing  is  due  to 
the  action  of  the  governor,  and  is  always  to  be  expected. 


INDICATORS    AND    INDICATOR    CARDS.  135 

Too  Great  an  Expansion  is  indicated  by  the  expansion 
line  extending  down  below  the  initial  back  pressure  and 
forming  a  loop,  as  shown  at  j^  in  Fig.  59.  The  pressure 
of  the  steam  at  the  end  of  the  stroke  is  less  than  the 
initial  back  pressure,  and  when  the  exhaust  valve  is 
opened  the  pressure  in  the  cylinder  is  raised  instead  of 
being  lowered. 

The  area  of  the  loop  at  345,  must  be  subtracted  from 
the  area  1256.  The  small  loop  means  negative  work ; 
since,  while  the  loop  is  being  formed,  the  forward  pressure 


Fg.  59. 

on  the  piston  is  less  than  the  back  pressure.  In  measur- 
ing the  area  of  such  a  card  with  the  planimeter,  the 
instrument  will,  of  itself,  subtract  the  area  of  the  small 
loop,  if  the  tracing  point  be  moved  down  and  around 
over  the  expansion  line  just  as  the  pencil  moved  when 
the  loop  was  formed. 

Early  Admission,  which  is  a  result  of  too  much  lead,  is 
indicated  by  the  line  61,  in  Fig.  60,  slanting  backwards, 
and  by  the  sharp,  backward-pointing  beak  at  I. 

Early  Release  is  indicated  by  the  line  34,  in  Fig.  60, 
slanting  forward,  and  by  the  sharp,  forward-pointing  beak 
at  4. 

In  the  case  of  engines  with  single  valves,  early  release 
will,  if  the  valve  is  properly  made,  always  accompany 
early  admission,  but  in  the  case  of  engines  that  have 


136  STEAM    ENGINES    AND    BOILERS. 

separate   steam   and  exhaust  valves,  early  release    need 
not  accompany  early  admission. 


Fig.  60. 

In  the  case  of  single  valve  engines,  early  admission 
and  early  exhaust  may  be  corrected  by  turning  the  eccen- 
tric backward  on  the  shaft,  so  as  to  reduce  the  angle  of 
advance. 

When  there  are  separate  exhaust  and  steam  valves,  the 
manner  of  correcting  early  admission,  or  early  exhaust, 
depends  upon  the  valve  gear. 

Late  Admission,  which  is  a  result  of  too  little  lead,  is 
indicated  by  the  line  61,  in  Fig.  61,  slanting  forward,  and 
by  the  sudden  rounding  at  6. 

Late  Release  is  indicated  by  the  line  34,  in  Fig.  61, 
slanting  backward,  and  by  the  sharp,  beak-like  point 
at  3. 

When  the  exhaust  and  admission  are  controlled  by  the 
same  valve,  late  release  will  always,  if  the  valve  is  prop- 
erly designed,  accompany  late  admission ;  both  may  be 
corrected  by  turning  the  eccentric  forward  on  the  shaft, 
so  as  to  make  the  angle  of  advance  greater. 

Where  there  are  separate  exhaust  and  steam  valves, 
late  exhaust  need  not  accompany  late  admission,  and  the 


INDICATORS    AND    INDICATOR    CARDS. 


137 


manner  of  correcting  either  will  depend  upon  the  valve 
gear. 


Fig.  61. 

Too  Great  Compression  is  shown  by  the  compression 
line  being  carried  above  the  initial  line  of  pressure  and 
forming  a  loop,  as  shown  at  I  in  Fig.  62. 


Fi?.  62. 

This  can  sometimes  be  remedied  by  turning  the  eccen- 
tric backward,  so  as  to  make  the  angle  of  advance  less. 
Where  there  are  separate  steam  and  exhaust  valves,  the 


138  STEAM    ENGINES    AND    BOILERS. 

exhaust  valves  must  be  changed  so  that  they  will  not 
close  so  early  in  the  return  stroke. 

Leak  During  Compression  is  indicated  by  a  break  in 
the  compression  line,  as  shown  at  67  in  Fig.  63. 

In  case  a  card  such  as  shown  in  Fig.  63  is  obtained,  the 
piston  should  be  tested  for  tightness.  To  do  this,  remove 
the  head  of  the  cylinder,  after  the  steam  has  been  shut 
off,  and  block  the  engine  in  such  a  position  that  the  steam 
port  admitting  steam  to  the  crank  end  of  the  cylinder  is 
open;  then  turn  on  the  steam  and  note  whether  or  not 


any  passes  the  piston.  If  the  piston  leaks  it  should  be 
made  tight  at  once. 

If  the  piston  is  tight  and  all  the  drip  cocks  are  closed 
tight,  a  break  in  the  compression  line,  as  shown  at  67  in 
Fig.  63,  indicates  a  leak  from  the  cylinder  into  the 
exhaust  port. 

Leak  During  Expansion.  In  order  to  determine 
whether  or  not  there  is  any  leakage  into,  or  out  of,  the 
cylinder  during  expansion,  it  is  necessary  to  draw  the 
theoretical  expansion  line  as  follows  : — 

In  Fig.  64,  let  AB  be  the  atmospheric  line;  AAi  be 
equal  to  the  atmospheric  pressure,  according  to  the 
scale  of  pressures  of  the  card  ;  and  let  O  be  the  "  origin  " 
of  the  card,  found  from  the  compression  line  by  the 
method  described  in  Art  55. 


INDICATORS    AND    INDICATOR    CARDS. 


139 


Take  any  point,  c,  on  the  expansion  line,  close  to  the 
point  of  cut-off;  through  it  draw  Cc  parallel  to  AB,  and 
cD  perpendicular  to  AB.  Care  must  be  taken  to  choose 
the  point  c  in  such  a  position  that  there  can  be  no  doubt 
but  that  the  steam  valve  is  closed. 


IB. 


Fig.  64. 

Through  O  draw  any  line  intersecting  Cc,  at  n,  and 
cD,  at  m.  Draw  through  n  a  line  perpendicular  to  AB, 
and  continue  it  until  it  intersects,  at  ft  a  line  drawn 
through  m  parallel  to  AB. 

The  point /is  a  point  on  an  equilateral  hyberbola,  here 
assumed  to  be  the  theoretical  expansion  line.  By  repeat- 
ing the  construction,  any  number  of  points  may  be  found 
on  the  desired  curve ;  and  the  curve  may  afterwards  be 
drawn  in. 

Let  cd  be  the  theoretical  expansion  line.  If  the 
expansion  line  of  the  indicator  card  is  below  the  theoret- 
ical line,  it  indicates  condensation  or  leakage  out  of  the 
cylinder,  or  both ;  while,  if  the  expansion  line  of  the  card 
is  above  the  theoretical  line,  it  indicates  leakage  of  steam 
past  the  steam  valve  into  the  cylinder. 


140 


STEAM    ENGINES    AND    BOILERS. 


Where  the  number  of  times  the  steam  is  expanded  is 
large,  the  expansion  line  of  the  card  will  always  fall  below 
the  theoretical  line.  This  is  due  to  the  fact  that,  for  a 
large  number  of  expansions,  the  expansion  line  is  not  an 
equilateral  hyperbola,  as  has  been  assumed  in  this  work. 


Fig.  64a. 


Indicator  Cord  too  Long.  When  the  cord  connecting 
the  drum  of  the  indicator  to  the  reducing  motion  is  too 
long  the  drum  is  allowed  to  move  back  and  come  to  rest 
before  the  piston  gets  to  the  head  end  of  its  stroke.  The 
effect  of  this  on  the  card  is  as  shown  in  Fig.  64a.  On  the 
card  from  the  head  end  of  the  cylinder,  marked  Ht  there 
appears  the  vertical  line  12;  and  on  the  card  from  the 
crank  end  of  the  cylinder,  marked  C,  there  appears  the 
vertical  line  34. 


CHAPTER  VII 

COMPOUND  ENGINES  AND  CONDENSERS. 

58.  COMPOUND  ENGINES. —  While  any  engine  in  which 
the  steam  is  used  in  more  than  one  cylinder  is  a  com- 
pound engine,  the  term  has  come  to  be  restricted,  by 
custom,  to  those  engines  in  which  the  steam  is  used  in 
but  two  cylinders,  a  high  pressure  cylinder  and  a  low 
pressure  cylinder.  The  steam  enters  the  high  pressure 
cylinder  on  leaving  the  boiler,  and  there  expands  a  certain 
number  of  times ;  after  leaving  the  high  pressure  cylinder 
the  steam  passes  into  the  low  pressure  cylinder,  where  it 
is  expanded  more.  By  using  two  cylinders  for  a  given 
number  of  expansions,  the  number  of  expansions  in  each 
cylinder  is  made  much  less  than  it  would  be  if  there  were 
but  one  cylinder,  and,  therefore,  the  range  of  pressures 
in  each  cylinder  is  made  less.  As  the  range  of  tempera- 
tures, of  expanding  steam,  depends  upon  the  range  of 
pressures,  the  use  of  two  cylinders,  to  obtain  a  given 
number  of  expansions,  will  reduce  the  range  of  tempera- 
tures in  each  cylinder. 

The  losses  in  an  engine  are  always  of  two  kinds, 
thermodynamic  and  mechanical. 

The  thermodynamic  losses  are  due  to  radiation  of  heat 
from  the  walls  of  the  cylinder,  and  the  heating  of  the 
metal  of  the  cylinder;  they  bring  about  an  increase  in  the 
comsumption  of  steam,  per  horse  power  per  hour,  by 
condensing  the  steam  in  the  cylinder.  It  has  been  found 
that  the  condensation  of  steam  in  a  cylinder  is  decreased 
by  well  lagging  the  cylinder  with  non-conducting 
materials  ;  by  increasing  the  speed  of  rotation  of  the 
engine,  thus  decreasing  the  length  of  time  each  particle 

(141) 


142  STEAM    ENGINES    AND    BOILERS. 

of  steam  is  in  contact  with  the  metal  of  the  engine  ;  by 
reducing  the  number  of  expansions  in  the  cylinder,  thus 
reducing  the  range  of  temperatures  of  the  steam  during  ex- 
pansion ;  and,  finally,  by  decreasing  the  radiating  surface 
of  the  cylinder. 

The  mechanical  losses  are  due  to  the  friction  of  the 
moving  parts,  and  are  decreased  by  good  workmanship 
and  materials  in  construction ;  by  reducing  the  number 
of  moving  parts  ;  and  by  care  and  good  management 
while  running. 

The  whole  object  of  compounding  is  to  reduce  the 
amount  of  steam  used,  per  horse-power  per  hour,  by 
reducing  the  losses  in  the  engine.  As  the  lagging  of  a 
simple  engine  can  be  made  just  as  good  and  efficient  as 
that  of  a  compound  engine,  there  can  be  no  reduction 
of  losses  on  that  account;  the  speed  of  rotation  of  the 
simple  engine  may  be  just  as  great  as  that  of  the  com- 
pound, and,  therefore,  there  can  be  no  reduction  on  that 
account;  two  cylinders  expose  more  surface  for  radiation 
than  one,  and  therefore,  compounding  increases  the  losses 
due  to  this;  but  the  range  of  expansion  in  each  cylinder 
of  a  compound  engine  is  less  than  it  would  be  in  a  single 
cylinder  engine  of  the  same  total  number  of  expansions, 
and  there  is,  then,  a  reduction  of  loss  in  the  compound 
engine  on  this  account. 

The  mechanical  losses  may  be,  and  usually  are,  greater 
in  the  compound  engine  of  the  same  power  than  they  are 
in  the  single  cylinder  engine. 

Summing  up  then,  the  compound  engine  tends  to 
increase  the  thermodynamic  losses  by  increasing  the  radi- 
ating surface,  and  also  tends  to  increase  the  mechanical 
losses  by  increasing  the  number  of  moving  parts  ;  but  it 
tends  to  decrease  the  thermodynamic  losses  by  decreas- 
ing the  range  of  temperatures  of  the  steam  in  the  cylinders, 
by  reducing  the  number  of  expansions  in  each. 

When  the  reduction  of  losses  is  greater  than  the  increase, 


COMPOUND    ENGINES    A^D    CONDENSERS.  143 

the  compound  engine  should  be  used.  With  low  pressures 
and  a  small  number  of  expansions,  the  single  cylinder 
engine  is  more  economical  than  the  compound  engine. 
It  is  probably  safe  to  say  that  for  pressures  under 
sixty  pounds,  by  the  gauge,  the  single  cylinder  condens- 
ing engine  is  more  economical  than  a  compound  engine; 
but  for  pressures  above  sixty  pounds,  by  the  gauge,  the 
compound  engine  is  more  economical.  The  higher  the 
pressure  and  the  greater  the  number  of  expansions,  the 
greater  is  the  economy  of  the  compound  engine  as  com- 
pared to  the  single  cylinder  engine.  In  the  case  of  non- 
condensing  engines  the  single  cylinder  engine  is  probably 
more  economical  for  all  pressures  under  ninety  pounds", 
by  the  gauge,  but  above  this  it  is  probable  that  the  com- 
pound engine  is  the  better  to  use. 

As  the  single  cylinder  engine  has  its  limit,  at  which  it 
becomes  less  economical  than  the  compound  engine,  so 
the  compound  engine  becomes  less  economical  than  the 
triple  expansion  engine,  where  the  steam  is  expanded 
successively  in  three  cylinders,  for  pressures  greater  than 
about  one  hundred  and  twenty  pounds  by  the  gauge. 

Up  to  about  four  expansions,  it  is  probable  that  the 
single  cylinder  engine  is  more  economical  than  the  com- 
pound engine  ;  for  from  four  to  six  expansions,  there  is 
not  much  choice  between  the  two  engines,  so  far  as 
economy  is  concerned ;  for  from  six  to  ten  expansions, 
the  compound  engine  is  the  more  economical.  For  a 
greater  number  of  expansions  than  ten,  it  will  usually  be 
found  better  to  use  a  triple  expansion  engine. 

Compound  engines  are  usually  classified  under  two 
heads,  viz.,  Tandem  Compound,  Cross-compound. 

59.  TANDEM  COMPOUND  ENGINES. —  Tandem  compound 
engines  are  those  which  have  the  two  cylinders  placed 
one  in  front  of  the  other.  There  are  two  pistons,  one  for 
each  cylinder;  one  piston  rod;  one  connecting  rod;  and 
one  crank.  The  steam  flows  as  directly  as  possible  from 


144  STEAM    ENGINES    AND    BOILERS. 

the  high  pressure  cylinder  into  the  low  pressure  cylinder, 
and  the  connecting  pipes  are  usually  made  small.  There 
is  no  "  receiver,"  or  vessel  into  which  the  steam  flows, 
between  the  high  pressure  cylinder  and  the  low  pressure 
cylinder. 

The  tandem  compound  engine  occupies  less  space  than 
the  cross-compound. 

60.  CROSS-COMPOUND  ENGINES. —  The  two  cylinders  of 
the  cross-compound  engine  are  placed  side  by  side,  and 
there  is  for  each  cylinder,  a  separate  piston  rod,  connect- 
ing rod,  cross-head,  and  crank.  The  steam  often  passes 
into  a  "  receiver  "  after  leaving  the  high  pressure  cylinder, 
and  there  remains  until  it  passes  into  the  low  pressure 
cylinder.  The  cranks  are  usually  set  at  an  angle  of  90° 
with  one  another ;  so  that  when  the  high  pressure  piston 
is  at  the  end  of  the  stroke,  the  low  pressure  piston  is  in 
mid-position  and  has  half  a  stroke  to  complete  before  it 
is  ready  to  take  steam ;  it  is  on  this  account  that  it  is 
always  necessary  to  have  a  receiver  for  cross-compound 
engines  whose  cranks  are  at  90°. 

The  cross-compound  engine  occupies  more  space  than 
the  tandem  compound  engine,  but  by  having  two  piston 
rods,  two  connecting  rods,  and  two  cranks,  it  really  be- 
comes equivalent  to  two  engines  connected  to  the  same 
shaft,  each  of  which  need  be  only  about  half  the  power  of 
the  single  cylinder  engine  to  do  the  same  work.  And, 
therefore,  all  the  parts  of  the  cross-compound  engine 
may  be  lighter  and  smaller  than  the  same  parts  on 
either  a  single  cylinder  engine  or  a  tandem  compound 
engine. 

The  twisting  effort  of  the  crank  shaft  is  made  more  uni- 
form by  having  the  cranks  at  90°,  as  when  one  piston  is 
exerting  its  maximum  effort  the  other  is  exerting  a  much 
less  effort,  and,  therefore,  the  engine  becomes  easier  to 
govern. 


COMPOUND    ENGINES    AND    CONDENSERS.  145 

61.  RATIO  OF   CYLINDERS   OF   COMPOUND  ENGINES. — 
The  ratio  of  the  volume  of  the    low   pressure   cylinder 
to  the  volume   of  the  high  pressure  cylinder  may  be  de- 
noted by  K,  and,  since  the  strokes  of  the  two  cylinders 
of  a  compound  engine  are  usually  the  same,  we  have 

jyi 
K  =   —p.     Where  D  is  the  diameter  of  the  low  pressure 

cylinder,  and  d  the  diameter  of  the  high  pressure  cylinder. 
The  value  of  K  ought  to  be  made  to  vary  with  the 
pressure  of  the  steam  and  the  number  of  times  the  steam 
is  expanded.  Designers  usually  try  to  make  the  value  of 
K  such  that  the  "  drop,"  or  fall  in  pressure  of  the  steam 
between  the  high  pressure  cylinder  and  the  low  pressure 
cylinder,  shall  be  small,  when  the  work  of  the  engine 
is  divided  so  that  it  is  the  same  in  each  cylinder. 

The  value  of  ./T  varies  from  2j  to  4  for  automatic  high 
speed  engines;  and  from  3  to  4^  for  engines  of  the 
Corliss  type ;  it  is  always  equal  to  the  quotient  obtained 
by  dividing  the  total  number  of  times  the  steam  is 
expanded  by  the  number  of  times  it  is  expanded  in  the 
high  pressure  cylinder. 

62.  THE  HORSE-POWER    OF  COMPOUND  ENGINES. —  In 
determining  the  horse-power  of  a  compound  engine  from 
which  indicator  cards  have  been  taken,  work  up  the  card 
for  each  cylinder  just  as  if  it  were  the  card  from  a  single 
cylinder   engine;  and   having  found  the  mean   effective 
pressure  for  each  cylinder,  calculate  the  horse-power  of 
each  by  the  method  explained,  in  Art.  54,  for  a  single 
cylinder  engine.     The  sum  of  the  horse-powers  developed 
in  the   two   cylinders   will   be   the  horse-power   of  the 
engine. 

In  calculating  the  horse-power  that  a  compound  engine 
ought  to  develop,  for  given  conditions  as  to  absolute 
steam  pressure,  total  number  of  expansions  of  the  steam, 
number  of  strokes  per  minute,  diameters  of  low  and  high 

10 


146  STEAM    ENGINES    AND    BOILERS. 

pressure  cylinders,  and  length  of  stroke,  proceed  as  if 
there  were  but  one  cylinder,  of  the  same  size  as  the  low 
pressure  cylinder,  in  which  the  total  expansion  of"  the 
steam  took  place.  If  the  horse-power  obtained  by 
assuming  that  all  the  work  was  done  in  the  low  pressure 
cylinder  be  multiplied  by  a  factor,  whose  value  depends 
upon  the  type  of  the  compound  engine,  the  result  will  be 
equal  to  the  horse-power  the  compound  engine  ought  to 
develop  under  the  given  conditions. 

Let  A  be  the  area,  in  square  inches,  of  the  low  pressure 
piston  ;  L,  its  length  of  stroke,  in  feet  ;  Nt  the  number  of 
strokes  made  by  the  low  pressure  piston  per  minute  ;  £, 
the  total  number  of  times  the  steam  is  expanded  in  the 
compound  engine  ;  and  C,  a  factor  whose  value  depends 
upon  the  type  of  the  compound  engine.  The  horse- 
power of  the  engine  will  be  given  by  the  equation 


Pe  is  the  mean  effective  pressure,  which,  by  substituting 
E  for  r  in  (50),  is  found  to  be 


PI  is  equal  to  the  gauge  pressure  of  the  steam  in  the 
boiler  plus  14.7.  P3  is  the  average  back  pressure,  and  may 
be  assumed  to  be  between  two  and  a  half  and  five  pounds 
per  square  inch,  for  condensing  engines. 

The  value  of  the  factor  C  will  vary  from  0.75  to  0.90 
for  automatic  high-speed  engines,  and  from  0.80  to  0.90 
for  engines  of  the  Corliss  type. 

63.  CONDENSERS. —  Condensers  are  usually  associated 
in  the  minds  of  most  people  with  compound  engines, 


COMPOUND    ENGINES    AND    CONDENSERS.  147 

although  there  is  no  reason  why  a  condenser  should  not 
be  used  with  a  single  cylinder  engine,  provided  there  is  a 
good  supply  of  water. 

There  are  two  kinds  of  condensers  in  use  at  present,  viz., 
the  jet  condenser  and  the  surface  condenser. 

The  jet  condenser  is  more  generally  used  on  land, 
because  it  is  simpler ;  not  so  apt  to  get  out  of  repair ;  and, 
where  the  water  is  good,  gives  as  good  results  as  the 
surface  condenser,  if  not  better.  When  the  jet  con- 
denser is  used,  the  exhaust  steam  from  the  engine  enters 
the  "  condensing  chamber,"  where  it  comes  in  contact 
with  the  condensing  water,  in  the  form  of  spray,  and  is 
condensed.  The  condensed  steam,  together  with  the 
condensing  water,  is  pumped  out  of  the  "  condensing 
chamber  "  into  the  "  hot  well,"  by  means  of  a  pump  called 
the  "  air  pump."  Part  of  the  water  in  the  hot  well  is 
pumped  back  into  the  boiler  by  the  "  feed  pump,"  and 
the  remainder  is  allowed  to  run  to  waste. 

The  condensing  water  is  sprayed,  when  it  enters  the 
condensing  chamber,  by  means  of  a  rose  fixed  on  the  end 
of  the  injection  pipe,  or  by  means  of  a  perforated  plate, 
called  the  "spattering  plate,"  fixed  inside  of  the  con- 
densing chamber. 

The  principal  parts  of  a  jet  condenser  are,  the  con- 
densing chamber,  the  air  pump,  and  the  hot  well. 

The  air  pump  of  jet  condensers  is  sometimes  worked  by 
the  engine,  being  connected  to  it  by  a  belt,  but  is  often 
provided  with  an  independent  steam  cylinder  of  its  own. 
Condensers  whose  air  pump  is  worked  independent  of  the 
engine  are  known  as  "  independent  condensers."  Con- 
densers of  this  class  will  pump  their  own  condensing 
water ;  but  they  ought  not  be  expected  to  draw  water 
more  than  12  or  15  feet,  as  there  are  a  great  number  of 
joints  about  a  condenser  that  are  often  difficult  to  keep 
tight,  and  the  water  flows  into  the  condensing  chamber 
against  whatever  pressure  there  may  be  there.  The 


148 


STEAM   ENGINES    AXD    BOILERS. 


smaller  the  height  through  which  the  air  pump  lifts  the 
condensing  water,  the  better  will  the  condenser  work. 

In  Fig.  65  is  shown  a  section  of  an  "  independent  con- 
denser." A  is  the  steam  inlet ;  B  is  the  water  inlet ;  Fis 
the  condensing  chamber  ;  G  is  the  air  pump,  worked  by 
the  steam  cylinder  K ;  and  J  is  the  outlet  to  the  hot  well. 


Fig.  65. 
Worthington  Independent  Condenser. 

When  the  surface  condenser  is  used,  the  condensing 
water  passes  through  a  number  of  small  copper  or  com- 
position tubes,  on  the  outside  of  which  the  steam  to  be 
condensed  circulates.  The  steam  coming  in  contact  with 
the  cold  surface  of  the  tubes  is  condensed  and  falls  to 
the  bottom  of  the  condenser,  from  where  it  is  pumped,  by 
the  "  air-pump,"  into  the  hot  well.  The  condensing 


COMPOUND    ENGINES    AND    CONDENSERS. 


149 


water  is  either  drawn  or  forced  through  the  condenser 
tubes  by  the  "  circulating  pump." 

The  surface  of  the   tubes  in  contact  with   the   steam 
forms   the  condensing   surface   of  the   condenser.     The 


tubes  are  always  of  very  small  diameter,  and  the  metal  of 
which  they  are  made  is  as  thin  as  is  consistent  with  safety. 
Sometimes,  instead  of  the  steam  circulating  on  the  outside 
of  the  tubes,  it  passes  through  them,  and  the  condensing 
water  circulates  on  the  outside. 

The  principal  parts  of  the  surface  condenser  are  :  the 


150  STEAM    ENGINES    AND    BOILERS. 

condensing  surface,  being  the  surface  of  a  great  number 
of  very  small  tubes  ;  the  air  pump  ;  the  circulating  pump  ; 
and  the  hot  well. 

The  great  point  in  favor  of  the  surface  condenser  is  the 
fact  that  the  steam,  after  being  condensed,  is  returned  to 
the  boiler  and  used  again  without  coming  in  contact  with 
the  condensing  water.  The  same  water  for  making  steam 
is  used  over  and  over  in  the  boiler,  without  any  new  feed 
water  except  what  is  necessary  to  supply  the  loss  due  to 
leakage  of  the  boiler  and  the  various  connections  from 
the  boiler  to  the  engine  and  condenser.  As  but  little 
fresh  feed  water  is  needed,  the  boiler  may  be  kept  very 
free  from  scale  and  sediment.  This,  of  course,  is  a  great 
point  in  its  favor  for  use  at  sea,  or  where  the  water  is  bad 
and  likely  to  form  scale  in  the  boiler. 

The  main  objection  to  the  surface  condenser  was  that 
when  the  tubes  got  hot  they  expanded,  and  then  were 
likely  to  become  loose  and  leak.  They  were,  also, 
likely  to  "creep;  "  that  is,  work  out  of  the  bearing  at  one 
end.  Both  of  these  objections  have  been  overcome  in 
the  Wheeler  condenser,  shown  in  Fig.  66,  by  fastening 
the  tubes  at  one  end  only. 

An  explanation  of  this  condenser  is  unnecessary  as 
everything  is  clearly  shown  in  the  figure. 

64.  EFFECT  OF  THE  CONDENSER  ON  THE  POWER  OF  THE 
ENGINE. —  Condensing  the  exhaust  steam  from  an  engine 
diminishes  the  back  pressure  by  creating  a  partial  vacuum 
behind  the  piston.  This  vacuum  is  generally  spoken  of 
as  being  so  many  "inches  of  mercury;"  each  inch  of 
mercury  representing  a  diminution  of  about  half  a  pound 
in  the  back  pressure,  and  therefore,  a  corresponding  in- 
crease in  the  mean  effective  pressure  on  the  piston. 

It  is  seldom  that  the  vacuum  maintained  by  a  condenser 
will  exceed  26  inches  of  mercury,  while  the  usual  vacuum 
will  be  about  24  inches.  It  is  usual  to  assume  that  the 
difference  between  the  back  pressure  without  the  con- 


COMPOUND    ENGINES    AND    CONDENSERS.  151 

denser  and  the  back  pressure  with  the  condenser,  is  equal 
to  the  pressure  corresponding  to  the  vacuum  maintained 
by  the  condenser. 

The  equation  for  the  horse-power  of  an  engine  is,  from 

(54), 

PeLAN 

33000 

Now,  if  we  suppose  that  the  speed  of  the  engine  is  to 
be  the  same  after  the  condenser  is  attached,  as  it  was 
before,  L,  A,  and  N  will  be  constants  and  the  horse- 
power will  vary  directly  as  P&  varies.  From  equation  (50) 
we  have 

(65)  P.  =  P,  0  +  *«P^-0  _  P, 

If  /a  is  the  average  back  pressure  without  the  con- 
denser; P'z,  the  average  back  pressure  with  the  con- 
denser ;  /e,  the  mean  effective  pressure  without  the 
condenser;  P'e,  the  mean  effective  pressure  with  the 
condenser  ;  H.  P.,  the  horse-power  of  the  engine  without 
the  condenser  ;  and  H'  .  P'.,  the  horse-power  with  the  con- 
denser; we  have 


p  fl  +  hvp-  l°y-  r\  - 
(66)        *••  f-      r. 


H.    P.        VJe         p    /  1  +  ]>np.  log.  r\  _    p 

1      ~~  ~  " 


Equation  (66)  shows  how  many  times  greater  the  horse- 
power of  the  engine  is  with  a  condenser  than  it  is  with- 
out a  condenser. 

Suppose  that  it  is  desired  that  the  power  of  the  engine 
should  not  be  increased,  but  that  it  should  remain  the 
same,  and  that  the  cut-off  should  change  so  that  the 
engine  will  use  less  steam  with  the  condenser  than  without 
it.  Let  rbe  the  number  of  times  the  steam  is  expanded 
without  the  condenser,  and  r',  the  number  of  times  it  is 
expanded  with  the  condenser. 

In  this  case  we  have  H.  P.  =  H'.  P'.,  and,  therefore, 
Pe  =  P'  or 


152  STEAM   ENGINES    AND    BOILERS. 


(67)  pi(l+?W.  l°9-r)  _ 

r 

r,    (1  +  hyp.  loq.  r') 

•*  i — -, '- —  ./   3. 

From  this  we  get 

(68)  1  +  l*yp*  log-  r'  __  1  +  ft?//?,  toff,  r        (P3  — p^) 

This  equation  can  be  solved  by  trial,  using  Table  2.  If 
there  were  no  clearance  to  the  engine  and  Fwere  the 
volume  in  cubic  feet  of  the  cylinder  of  the  engine,  the 
volume  of  the  steam  used  per  stroke  without  the 

Y 

condenser  would  be  — ;  and    the    volume    used   with  the 
r 

condenser  would  be  — ,     The  fraction  of  saving  would  be 

Z        Z 

(69)  y  =  L *—=i—  r-. 

•     r 

From  y,  given  by  (69),  must  be  subtracted  the  fraction 
obtained  by  dividing  the  quantity  of  steam  required  to  run 

Y 

the  condenser  by  -. 
r 

If,  instead  of  increasing  the  work  done  by  the  engine 
or  changing  the  cut-off,  it  should  be  desired  that 
the  engine  should  do  the  same  work  with  the  condenser, 
and  cut-off  at  the  same  point,  that  it  did  without  the 
condenser,  but  use  a  lower  absolute  pressure  of  steam  in 
the  boiler,  we  would  have,  since  Pe  =  P'e  and  the  value 
of  r  is  not  changed, 

fnc\\  -D   (1  H~  hyp.  log.  r) 

(70)  ^i-          — —  -P%  = 

jy,  (1  -{-hyp.log.  r)         „ 


COMPOUND    ENGINES    AND    CONDENSERS.  153 

P'l  is  the   absolute   boiler  pressure  that   is  carried  when 
the  condenser  is  used. 
From  (70)  we  have 

,  (A  —  P's)  r 


65.  AMOUNT  OF  CONDENSING  WATER  REQUIRED. —  The 
number  of  pounds  of  water  required  to  condense  one 
pound  of  steam  depends  upon  the  temperature  of  the 
steam  when  it  leaves  the  engine,  and  upon  the  initial  and 
final  temperatures  of  the  condensing  water.  The  tem- 
perature of  the  steam  when  it  leaves  the  engine  depends 
upon  the  absolute  pressure,  P2,  of  the  steam  at  the  end  of 
the  forward  stroke,  j  ust  before  the  exhaust  valve  is  opened. 
The  expression  for  this  final  absolute  pressure  may 

n 

for  all  ordinary  purposes  be  taken  as  P2  =  —    PI  is  the 

initial  absolute  pressure   of  the  steam,  and  r  is  the  num- 
ber of  times  the  steam  is  expanded. 

The  gauge  pressure  of  the  steam,  or  pressure  above 
the  atmosphere,  when  it  enters  the  condenser  is  PI  — 

14.7- 

Let  /  be  the  latent  heat  of  one  pound  of  steam  at  a 
gauge  pressure  of  Pz  —  14.7,  and  t\  the  corresponding 
temperature.  The  values  of  /  and  t\  may  be  obtained 
from  Table  I.  Also,  let  fa  be  the  initial  temperature  of 
the  condensing  water,  and  fa  the  final  temperature. 

The  heat  given  out  by  one  pound  of  the  steam  when  it 
condenses  will,  evidently,  be  /  +  t\  —  fa\  and  the  heat 
taken  up  by  every  pound  of  the  condensing  water  will  be 
/a  — fa\  therefore,  the  number  of  pounds,  W,  of  water 
required  to  condense  one  pound  of  steam  from  the  engine 
will  be, 

I  4-  ti  —  *8 


(72)  W  = 


ta  — 


154  STEAM    ENGINES    AND    BOILERS. 

4  should  be  taken  as  110°,  for  the  ordinary  work  of 
condensers. 

The  value  of  fa  depends  upon  the  source  of  supply  of 
the  water  and  the  climate  of  the  location  of  the  engine  ; 
it  will  be  greater  in  summer  than  in  winter.  It  will 
usually  be  safe  to  take  the  value  of  fa  as  80°. 


CHAPTER     VIII. 

HEAT  AND  COMBUSTION  OF  FUEL. 

66.  STEAM  MAKING. —  The  steam  used  in  an  actual 
engine  is  made  in  an  apparatus  that  is  often  spoken  of  as 
the  boiler  or  the  boiler  plant.  It  consists  of  three  main 
parts,  each,  in  a  manner,  dependent  upon  the  other  two, 
and  yet  in  many  ways  distinct  from  them.  These  parts 
are,  the  furnace,  the  boiler  proper,  and  the  chimney. 

In  Fig.  67  is  shown  a  section  of  a  furnace  and  boiler 
such  as  is  in  common  use  everywhere  in  this  country. 
The  various  parts  are  lettered  so  that  their  relations  to 
one  another  may  be  seen  at  once. 

The  part  termed  the  furnace  is  the  part  in  which  the 
heat,  afterwards  converted  by  the  engine  into  work,  is 
generated  by  the  combustion  of  fuel. 

The  boiler  is  simply  a  closed  vessel  which  contains  the 
water  of  which  the  steam  used  in  the  engine  is  formed. 
The  boiler  may  be  of  any  shape  or  size. 

The  chimney  is  the  part  which  carries  off  the  products 
of  combustion. 

The  fuel  is  put  in  the  furnace  on  the  grate,  and  is  there 
burned.  During  the  combustion  of  the  fuel  heat  is  gen- 
erated; a  part  of  this  heat  is  given  directly  to  the  boiler, 
by  radiation  from  the  hot  fuel,  and  a  part  is  carried  off  by 
the  gases  generated  by  the  combustion.  These  gases 
pass  out  of  the  furnace  into  the  chimney,  and  from  there 
they  pass  into  the  air.  On  the  way  from  the  furnace  to 
the  chimney,  the  hot  gases  are  made  to  come  in  contact 
with  the  boiler  ;  and  as  the  boiler  is  cooler  than  the  gases, 
a  part  of  the  heat  they  contain  is  given  up  to  it.  The 
heat  thus  obtained  by  the  boiler  is  transmitted  to  the 

(155) 


156 


STEAM   ENGINES    AND    BOILERS. 


water,  which  is  gradually  heated  and,   finally,  converted 
into  steam. 

The  dimensions  and  proportions  of  the  furnace  depend 


upon  the  heat  required  by  the  boiler  per  unit  of  time,  the 
kind  of  fuel,  and  the  type  or  kind  of  furnace. 

The  dimensions  and  proportions  of  the  boiler  depend 
upon  the  amount  of  steam  required  by  the  engine  per  unit 


HEAT  AND  COMBUSTION  OF  FUEL.         157 

of  time,  the    conditions  under  which   the   steam   is  gen- 
erated, and  the  type  of  the  boiler. 

The  dimensions  and  proportions  of  the  chimney  depend 
upon  the  kind  of  fuel,  the  amount  used  by  the  furnace 
per  unit  of  time,  and  the  temperature  at  which  the  hot 
gases  pass  off. 

67.  STEAM  REQUIRED  PER  HOUR. —  In  all  problems 
relating  to  boilers  it  is  necessary  to  know,  as  a  basis  upon 
which  to  design  the  furnace,  the  boiler  and  the  chimney, 
the  number  of  pounds  of  steam  required  per  hour  and  the 
conditions  under  which  it  must  be  made. 

If  we  are  designing  a  boiler  to  supply  steam  for  an  en- 
gine of  given  dimensions  and  power,  using  steam  at  a 
given  initial  gauge  pressure,  we  may  calculate  the  number 
of  pounds  of  steam  that  will  be  used  per  hour  by  the 
engine  and  to  this  add  a  per  cent  to  cover  leakage  and 
condensation,  and  thus  obtain  the  number  of  pounds  of 
steam  the  boiler  will  probably  be  called  upon  to  supply 
per  hour. 

From  (57)  of  Art.  24,  we  have  that  the  weight  of  steam 
used  per  stroke  by  an  engine  is 

LA 


144  r  s 

If  N  is  the  number  of  strokes  made  by  the  engine  per 
minute,  the  weight,  W\t  of  steam  used  by  the  engine  per 
minute  will  be 

(73)  Wi  =  N  S  = 


To  make  allowances  for  waste  from  various  sources,  for 
the  amount  of  steam  used  by  the  pumps,  and  for  that 
condensed  in  the  engine,  the  amount  of  steam  the  boiler 
ought  to  be  designed  to  supply  per  minute  may  be 

taken  as  —  W±.      As  the  steam  required  to  be  supplied 


158  STEAM    ENGINES    AND     BOILERS. 

per  hour  is  60  times  that  required  per  minute,  the  expres- 
sion for,  W,  the  number  of  pounds  of  steam  required  to 
be  supplied  by  the  boiler  per  hour  is 


,70  W  -  6°X8  IF.-- 

^     }  l~ 


144  r  a     ~     8rs 


68.  HEAT  REQUIRED  PER  HOUR. —  Having  assumed  or 
determined  the  number  of  pounds  of  steam  required  per 
hour,  it  is  next  necessary  to  determine,  if  it  is  not  already 
known,  the  pressure  by  the  gauge,  and  the  initial  temper- 
ature of  the  "  feed-water,"  or  water  entering  the  boiler. 

Let  P  be  the  pressure  per  square  inch,  by  the  gauge, 
of  the  steam  in  the  boiler ;  //",  the  total  heat  of  evapora- 
tion above  32°,  in  heat  units,  of  one  pound  of  steam  at  the 
gauge  pressure  P;  t,  the  initial  temperature  of  the  feed- 
water. 

H must  be  taken  from  Table  I  ;  while  /depends  upon 
the  source  of  supply  of  the  feed  water,  and  upon  con- 
siderations that  will  be  discussed  later. 

It  is  evident  that,  since  H  is  the  heat  required  to  raise 
the  temperature  of  one  pound  of  water  from  32°  to  the 
temperature  of  the  boiling  point  corresponding  to  the 
gauge  pressure  P  and  then  to  turn  the  water  into  steam, 
the  heat  required  to  raise  one  pound  of  water  from  a 
temperature  /  to  the  boiling  point  corresponding  to  P 
and  then  turn  it  into  steam,  will  be  H  — (t  —  32). 
The  heat  required,  then,  to  evaporate  H'7  pounds  of  water 
'per  hour,  under  the  given  conditions,  will  be 


(75)  Hi  =    W  [_H  —  (t  —  32)]. 


From  equation  (75),  it  is  evident  that,  for  a  given  value 
of  IV,  H\  will  be  smaller  as  we  make  H  smaller  and  as 
we  make  /larger,  and  hence  the  latter  should  always  be 
as  large  as  possible. 


HEAT   AND   COMBUSTION   OF   FUEL.  159 

The  value  of  H  depends  upon  the  pressure  by  the 
gauge  at  which  the  steam  is  formed  and  upon  nothing 
else;  and  as  is  seen  by  an  inspection  of  Table  I,  the 
higher  is  the  pressure  of  the  steam  in  the  boiler,  the 
greater  is  the  value  of  H.  It  is  also  seen,  however,  that 
the  value  of  H  increases  very  slowly  as  the  pressure  in- 
creases. Thus,  the  value  of  H  corresponding  to  a  pres- 
sure of  75  Ibs.,  by  the  gauge,  is  1179.4,  and  the  value  of  H 
corresponding  to  a  pressure  of  150  Ibs.,  by  the  gauge, 
is  1193.5  ;  so  that,  while  the  pressure  has  been  increased 
by  75  Ibs.,  H  has  been  increased  by  but  14.1  heat  units. 

The  value  of  /  depends  upon  the  source  of  supply  of 
the  feed-water  and  upon  whether  or  not  the  feed-water  is 
heated  before  it  is  forced  into  the  boiler.  It  is  customary 
to  force  the  feed-water  through  a  "  feed-water  heater " 
before  it  enters  the  boiler.  As  feed-water  heaters  will  be 
discussed  farther  along,  it  will  suffice  to  say  that  they  usu- 
ally consist  of  a  number  of  tubes,  surrounded  by  exhaust 
steam  from  the  engine,  through  which  the  feed-water  is 
forced  before  it  enters  the  boiler.  The  water,  while  pass- 
ing through  the  tubes  of  the  heater,  has  its  temperature 
raised  by  the  heat  imparted  to  it  by  the  exhaust  steam. 
The  heat  in  the  exhaust  steam  would  be  lost  if  it  were  not 
taken  by  the  feed- water;  so  that  the  feed- water  heater,  by 
raising  the  temperature  of  the  feed-water,  is  a  heat  saving 
appliance,  and  a  valuable  adjunct  to  any  engine  and 
boiler  plant,  where  there  is  exhaust  steam  escaping  into 
the  atmosphere. 

The  greater  /  is  made,  the  less  will  be  the  value  of  //i 
for  given  values  of  W and  H. 

Instead  of  speaking  of  the  number  of  heat  units  a 
boiler  will  require  per  hour  it  is  customary  to  speak  of 
"the  equivalent  water  from  and  at  212°"  that  it  will 
evaporate  per  hour. 

The  equivalent  water  from  and  at  212°  is  the  number 
of  pounds  of  water  that  could  be  evaporated  by  the  expend- 


160  STEAM    ENGINES    AND    BOILERS. 

iture  of  the  same  number  of  heat  units  actually  used  by 
the  boiler,  if  the  water  entered  the  boiler  at  212°  and  was 
converted  into  steam  at  a  temperature  of  212°. 

Since  the  heat  required  to  convert  one  pound  of  water 
at  a  temperature  of  212°,  into  steam  at  212°  is  equal  to 
the  latent  heat  of  water  at  atmospheric  pressure,  about 
966  heat  units,  it  is  seen  that  the  expression  for  "the 
equivalent  water  from  and  at  212°,"  Wot  is' 


The  factor   H  ~~  (t~  32)    is    called   the    "  factor     of 
966 

evaporation,"  and  may  be  defined  as,  the  factor  by  which 
the  water  actually  evaporated  by  a  boiler  must  be  multi- 
plied in  order  to  reduce  it  to  "  equivalent  water  from  and  at 

212.°  " 

In  Table  3  will  be  found  factors  of  evaporation  for 
different  gauge  pressures  of  steam  and  different  tempera- 
tures of  feed  water. 

Equation  (76)  gives  us  a  means  of  determining  the 
heat  required  per  hour  for  a  boiler,  when  we  know  the 
equivalent  water  from  and  at  2  1  2°  required  to  be  evaporated 
per  hour.  As  will  be  seen  later,  boilers  are  often  assumed 
as  being  able  to  evaporate  34}  Ibs.  of  water  from  and  at 
2  1  2°  per  hour  per  horse-power.  Upon  this  assumption, 
WQ  =  34^  B,  where  B  is  the  horse-power  of  the  boiler, 
and  the  expression  for  H\  becomes, 

(77)  J3i  =  966  W0  =  33327  B. 

69.  FUEL  REQUIRED  PER  HOUR.  —  The  number  of 
pounds  of  fuel  required  to  supply  the  heat  necessary  for 
the  boiler  per  hour,  depends  upon  the  heat  developed  by 
the  combustion  of  one  pound  of  the  fuel  and  upon  the 
amount  of  heat  that  is  lost,  in  various  ways,  by  the  furnace, 


HEAT  AND  COMBUSTION  OF  FUEL.         161 

the  boiler  and  the  chimney.  If  we  take  the  amount  of  heat 
developed  by  the  combustion  of  one  pound  of  the  fuel 
and  from  this  quantity  subtract  the  amount  that  is  lost, 
we  shall  obtain  the  quantity  of  heat  used  by  the  boiler 
per  pound  of  fuel ;  and  the  total  quantity  of  heat  required 
per  hour  divided  by  the  quantity  used  per  pound  of  fuel 
will  give  us  the  number  of  pounds  of  fuel  that  must  be 
burned  per  hour  in  the  furnace. 

It  is  evident,  therefore,  that  it  is  extremely  important 
that  we  should  know  the  amount  of  heat  developed  by 
the  complete  combustion  of  one  pound  of  the  fuel  in  the 
furnace. 

Combustion  may  be  defined  as  a  rapid  oxidation,  accom- 
panied by  the  evolution  of  light  and  heat. 

In  all  fuels  there  are  certain  elements  that  will  not 
burn,  but  which  remain  after  combustion  and  form  ash; 
and  there  are  other  elements  that  are  in  the  fuel  in  such 
small  quantities  that  their  presence  may  be  neglected. 
The  principal  elements  in  all  fuels,  whether  gaseous, 
liquid,  or  solid,  are  carbon,  hydrogen  and  oxygen. 

The  carbon  may  be  present  either  in  a  free,  uncom- 
bined  state  or  in  combination  with  a  part  of  the  hydrogen. 

The  hydrogen  is  always  present  either  in  combination 
with  the  oxygen  or  with  a  part  of  the  carbon.  We  always 
assume  that  a  part  of  the  hydrogen  is  in  combination  with 
all  of  the  oxygen,  and  that  the  rest  is  in  some  sort  of 
combination  with  part  of  the  carbon. 

It  is  generally  assumed  that  the  oxygen  in  a  fuel  is  in 
combination  with  a  part  of  the  hydrogen,  and  is  present 
as  water.  The  oxygen,  of  course,  does  not  burn,  but 
simply  reduces  the  amount  of  hydrogen  that  is  available 
for  combustion. 

Upon  combustion,  the  carbon  in  a  fuel  may  form  one 
of  two  compounds  : — 

I.  If  the  combustion  is  complete,  every  atom  of  the 
carbon  will  take  up,  and  enter  into  combination  with,  two 

11 


162  STEAM   ENGINES   AND    BOILERS. 

atoms  of  oxygen  and  form  carbon  dioxide,  or  carbonic 
acid  gas  as  it  is  sometimes  called,  whose  chemical  symbol 
is  CO*. 

2.  If  there  is  a  lack  of  oxygen  and  the  combustion  is 
not  complete,  every  atom  of  the  carbon  will  combine 
with  one  atom  of  oxygen  and  form  carbon  monoxide, 
whose  chemical  symbol  is  CO. 

It  has  been  determined  by  experiments  that  when  one 
pound  of  carbon  is  completely  burned,  so  as  to  form 
carbon  dioxide,  there  is  evolved,  by  the  combustion, 
14,500  heatunits  ;*  also,  thatwhen  one  pound  of  carbon 
is  burned  to  form  carbon  monoxide,  there  is  evolved 
4,400  heat  units.  Thus  there  is  a  difference  of  10,100 
heat  units  between  the  amounts  of  heat  evolved  by  the 
complete  and  the  partial  combustion  of  one  pound  of 
carbon.  It  is  customary,  in  all  discussions  as  to  the  heat 
of  combustion  of  fuels,  to  assume  that  all  the  carbon  in 
the  fuel  is  completely  burned  to  carbon  dioxide. 

Hydrogen,  when  burned,  enters  into  combination  with 
oxygen,  in  the  proportion  of  two  atom  of  hydrogen  to  one 
of  oxygen,  and  forms  water,  whose  chemical  symbol 
is  H*O. 

It  has  been  determined  by  experiments  that  one  pound 
of  hydrogen,  on  being  burned,  will  evolve  62,032  heat 
units,  or  about4.28  times  as  many  heat  units  as  are  evolved 
by  the  complete  combustion  of  one  pound  of  carbon. 
When  one  pound  of  hydrogen  burns  it  unites  with  eight 
pounds  of  oxygen ;  so  that,  with  the  oxygen  present  in 
any  fuel  there  is  always  united  one-eighth  of  its  weight  of 
hydrogen.  If,  then,  we  subtract  from  the  total  weight  of 
hydrogen  present  in  a  fuel,  one-eighth  of  the  weight  of 
the  oxygen,  the  remainder  will  be  the  weight  of  free 
hydrogen  in  the  fuel,  or  the  weight  of  hydrogen  that  will 
be  burned. 

To  obtain  the  theoretical  amount  of  heat  that  will  be 

*  The  heat  evolved  by  the  complete  combustion  of  one  pound  of  carbon 
varies  slightly  with  the  source  from  which  the  carbon  is  obtained,  and  recent 
experiments  have  shown  that  it  is  probably  nearer  14,600  than  14,500. 


HEAT    AND    COMBUSTION    OF   FUEL.  163 

evolved  by  the  combustion  of  one  pound  of  fuel,  it  is  nec- 
essary for  us  to  first  learn,  from  a  chemical  anaylsis,  the 
weights  of  carbon,  hydrogen,  and  oxygen  in  one  pound 
of  the  fuel.  The  weight  of  carbon  multiplied  by  14,500, 
will  give  the  number  of  heat  units  that  will  be  evolved  by 
the  complete  combustion  of  the  carbon ;  and  the  weight 
of  free  hydrogen,  equal  to  the  total  hydrogen  less  one- 
eighth  of  the  weight  of  the  oxygen,  multiplied  by  14,500 
times  4.28,  will  give  the  heat  that  will  be  evolved  by  the 
combustion  of  the  hydrogen  in  the  fuel.  The  sum  of  the 
heats  evolved  by  the  carbon  and  by  the  free  hydrogen 
will  be  the  total  heat  evolved  by  the  combustion  of  one 
pound  of  the  fuel.  Putting  what  has  been  said  in  mathe- 
matical language,  we  see  that  the  expression  for  the  the- 
oretical amount  of  heat,  h,  evolved  by  the  complete  com- 
bustion of  one  pound  of  fuel  is 

(78)  h  =  14500  [~C+  4.28  (  H'  —  - 

C  is  the  weight,  in  pounds,  of  carbon  in  one  pound  of 
the  fuel.  H'  is  the  weight,  in  pounds,  of  hydrogen  in  one 
pound  of  the  fuel.  O  is  the  weight,  in  pounds,  of  oxygen 
in  one  pound  of  the  fuel. 

Owing  to  the  fact  that,  in  most  fuels,  there  is  always  a 
small  quantity  of  substances,  other  than  carbon  and 
hydrogen,  that  burn  and  give  off  more  or  less  heat,  and 
that  a  part  of  the  total  heat  evolved  is  used  in  decompos- 
ing the  elements  before  they  can  burn,  the  theoretical 
amount  of  heat  obtained  by  the  use  of  equation  (78)  is 
not  exactly  equal  to  the  heat  actually  evolved  by  the 
combustion  of  one  pound  of  the  fuel.  Equation  (78), 
however,  may  be  used  when  no  other  means  is  at  hand 
for  determining  the  amount  of  heat  evolved  by  one  pound 
of  a  fuel. 

The  principal  fuels  used  in  boiler  furnaces  are  wood 
and  coal. 

Wood  is   seldom  used,   on   account  of  the    expense, 


164  STEAM    ENGINES    AND    BOILERS. 

except  in  special  establishments  where  the  refuse  con- 
sists largely  of  shavings,  saw-dusts,  and  pieces  of  wood 
that  must  be  got  rid  of.  In  such  cases,  of  course,  it  is 
much  better  and  cheaper  to  use  this  refuse  as  fuel  than  it 
is  to  buy  coal.  Wood  burns  rapidly  and  with  a  bright 
flame,  but  does  not  evolve  much  heat.  It  is  customary 
to  consider  one  pound  of  wood  equivalent  to  0.4  pounds 
of  coal. 

Coal  is  more  extensively  used  as  a  fuel,  in  boiler  fur- 
naces, than  any  other  substance.  Although  the  mining 
engineer  classifies  coal  into  several  groups  or  classes,  it 
will  suffice  for  us  to  consider  all  coal  used  in  boiler  fur- 
naces as  either  anthracite  or  bituminous  coal. 

Anthracite  coal  is  a  hard,  dense  coal  containing  a  large 
per  cent  of  carbon  and  a  small  per  cent  of  volatile 
matter;  it  is  slow  to  ignite  and  burns  at  a  high  tempera- 
ture with  little  or  no  visible  flame. 

Bituminous  coal  is  somewhat  soft  and  easily  broken ;  it 
usually  contains  from  20  to  50  per  cent  of  volatile 
matter ;  it  ignites  easily  and  burns  freely  with  quite  a 
flame. 

Coke  is  the  residue  obtained  after  distilling  off  the 
gases  from  certain  kinds  of  bituminous  coals;  it  is  not 
very  dense,  but  contains  a  high  per  cent  of  carbon. 

In  Table  4  is  given  the  heat  developed  by  the  complete 
combustion  of  one  pound  of  various  fuels. 

The  loss  of  heat  by  a  furnace,  boiler,  and  chimney 
may  be  ascribed  to  four  causes :  — 

1.  Incomplete  combustion. 

2.  Radiation. 

3.  Hot  gases  escaping  out  of  the  chimney. 

4.  Dropping  of  fuel  through  the  grate  into  the  ash-pit. 
The  loss  due  to  incomplete  combustion  is   the  most 

serious  of  all  losses.  It  may  be  that,  when  the  coal  is 
put  into  the  fire,  there  is  not  a  sufficient  amount  of  air  to 
burn  the  volatile  gases  that  pass  off,  so  that  the  greater 


HEAT  AND  COMBUSTION  OF  FUEL.         165 

part  of  them  will  not  be  burned.  Or,  it  may  be,  that 
owing  to  a  lack  of  air,  the  carbon  is  not  completely 
burned  to  carbon  dioxide,  but  is  burned  only  to  carbon 
monoxide.  If  the  carbon  is  not  completely  burned, 
there  is  a  loss  of  10,100  heat  units  for  every  pound  of 
carbon  converted  into  carbon  monoxide. 

The  loss  by  radiation  may  be  reduced  by  a  careful  and 
correct  setting  of  the  furnace  and  boiler,  and  by  taking 
precautions  to  have  just  as  little  hot  surface  exposed  as 
possjble. 

The  loss  due  to  the  hot  gases  escaping  up  the  chimney 
may  be  estimated  if  we  know  the  temperature,  t\,  of  the 
air  entering  the  furnace  and  the  temperature,  &,  of  the 
gases  entering  the  chimney.  The  specific  heat  of  one 
pound  of  chimney  gases  may,  without  serious  error,  be 
taken  as  equal  to  that  of  ordinary  atmospheric  air,  or 
0.24 ;  so  that  every  pound  of  gas  escaping  out  of  the 
chimney  carries  off  0.24  (fa  —  t\)  heat  units. 

The  heat  carried  off  by  the  gases  in  the  chimney  can- 
not be  said  to  be  wasted,  unless  there  is  some  fault  in  the 
design  of  the  boiler  plant,  as  this  heat  is  used  to  produce 
the  draft.  It  will  be  seen  later  that  the  amount  of  air 
entering  the  furnace  depends  upon  the  draft  of  the  chim- 
ney, which,  in  turn,  depends  upon  the  height  of  the  chim- 
ney and  upon  the  temperature  of  the  air  outside,  and  that 
of  the  gases  inside  of  the  chimney.  The  temperature  of 
the  gases  in  the  chimney  should  be  sufficient  to  produce 
the  required  draft,  and  no  more. 

The  loss  due  to  dropping  of  fuel  through  the  grate 
ought  not  to  be  large,  if  the  grate  is  properly  proportioned 
and  care  is  exercised  in  firing  the  furnace.  Some  loss, 
of  course,  is  always  bound  to  occur,  but  when  this  loss  is 
large  there  should  be  a  change  either  of  the  grate  or  fire- 
man, or  perhaps  of  both. 

The  sum  total  of  all  the  heat  lost  in  the  various  ways, 
per  pound  of  the  coal  consumed,  will  amount  to  from  20 


166  STEAM    EXGIXES    AND    BOILERS. 

to  50  per  cent  of  the  total  heat  of  combustion.  For  the 
best  boiler  plants,  where  care  is  exercised  in  firing,  the 
amount  of  heat  used  per  pound  of  coal  may  be  taken  as 
from  70  to  80  per  cent  of  the  heat  of  combustion ;  for 
good  boiler  plants  the  amount  may  be  taken  as  from  60 
to  70  per  cent  of  the  heat  of  combustion ;  and  for  poorly 
designed  plants,  poorly  fired,  the  amount  will  be  from  40 
to  60  per  cent  of  the  total  heat  of  combustion. 

Therefore,  if  K  represents  the  fraction  of  the  total  heat 
of  combustion  that  is  utilized,  the  heat  utilized  per  pound 
of  coal  will  be,  from  equation  (78), 


(79)    h0  =  Kh  =  1T1 4500     C  +  4.2 


If,  now,  we  divide  the  total  heat,  H\,  required  per  hour,  as 
given  in  (75)  or  (77),  by  the  heat  utilized,  ^0,  per  pound 
of  coal  we  obtain  the  amount  of  coal,  Ft  that  it  will 
be  necessary  to  burn  per  hour  in  the  furnace. 

Therefore,  the  expression  for 


(80) 


70.  AIR  REQUIRED  FOR  COMBUSTION.  —  The  air  admit- 
ted to  a  furnace  for  the"  combustion  of  a  fuel  is  a  me- 
chanical mixture,  consisting  principally  of  oxygen  and 
nitrogen  ;  these  gases  are  present  in  the  proportion,  by 
weight,  of  23  per  cent  of  oxygen  and  77  per  cent  of 
nirtogen  ;  by  volume,  the  proportion  in  which  they  are 
present  is  20  per  cent  of  oxygen  and  80  per  cent  of  nitro- 
gen. The  oxygen,  only,  is  used  in  combustion  ;  the 
nitrogen  is  inert,  and  so  far  as  aiding  combustion  is 
concerned,  is  useless. 

From  chemistry  we  learn  that  when  two  substances 
unite  chemically  they  always  do  so  in  a  certain  fixed 
proportion,  by  weight.  It  is  known  that  one  pound  of 


HEAT  AND  COMBUSTION  OF  FUEL.         167 

hydrogen  always  requires  eight  pounds  of  oxygen  for  its 
complete  combustion  into  water,  H^  0;  also,  that  one 
pound  of  carbon  requires  \  of  a  pound  of  oxygen  for  its 
combustion  to  carbon  monoxide,  CO,  and  f  of  a  pound 
of  oxygen  for  its  combustion  to  carbon  dioxide,  CO-2. 

Therefore,  if  we  assume  complete  combustion  of  the 
carbon  and  of  the  free  hydrogen,  the  number  of  pound? 
of  oxygen  required  per  pound  of  fuel  will  be, 


(81) 


C  is  the  total  carbon,  H*  the  total  hydrogen,  and  O  the 
total  oxygen  in  one  pound  of  the  fuel. 

Now,  since,  as  has  been  said,  there  is  only  23  per  cent, 
by  weight,  of  oxygen  in  the  air,  the  weight  of  air,  Ay 

required  to  supply  0\  pounds  of  oxygen  will  be,  A  =  -  —  „ 

Putting  for  Oi  its  value,  and  neglecting  fractions,  we  get 
the  following  expression  for  the  pounds  of  air  required 
for  the  complete  combustion  of  one  pound  of  fuel. 


(82)  A  =  12  C  -f  36  (  Hf  —  —  V 


Ordinarily,  we  may  assume  that  12  pounds  of  air  will 
be  needed  for  the  complete  combustion  of  one  pound  of 
coal;  and  as  one  pound  of  air  at  32°  occupies  a  volume 
of  I2j  cubic  feet,  the  volume  of  air,  at  32°,  required  for 
the  complete  combustion  of  one  pound  of  coal  may  be 
taken  as  150  cubic  feet. 

It  has  been  found  that  in  the  boiler  furnace  there  is 
always  needed  more  air  than  is  actually  necessary  for  the 
combustion  of  the  fuel,  in  order  to  dilute  the  gases  of 
combustion  and  to  make  sure  that  every  particle  of  hydro- 


168  STEAM    ENGINES    AND    BOILERS. 

gen  and  carbon  will  come  in  contact  with  the  amount  of 
oxygen  necessary  to  burn  it.  The  amount  of  air  for  dilu- 
tion, as  the  surplus  air  is  called,  depends  upon  how  inti- 
mately the  air  for  combustion  and  the  combustible  gases 
are  mingled  and  mixed.  It  has  been  found  that  it  is 
advantageous  to  have  the  air  enter  in  a  number  of  streams 
rather  than  in  a  large  body,  and  that  the  higher  the  veloc- 
ity of  the  entering  air  the  less  the  quantity  required  for 
dilution.  Experience  has  shown  that  in  the  case  of  nat- 
ural or  chimney  draft,  the  amount  of  air  required  for  dilu- 
tion will  be  about  equal  to  the  amount  required  for  com- 
plete combustion;  while  in  the  case  of  forced  draft,  the 
amount  of  air  required  for  dilution  will  be  about  equal  to 
one-half  that  required  for  combustion. 

Therefore,  we  may  say  that  for  chimney  draft  it  is  nec- 
essary to  supply  24  pounds  of  air  to  the  furnace  for  each 
pound  of  coal  burned;  and  for  forced  draft,  18  pounds 
of  air  are  required  per  pound  of  coal.  Of  course,  the 
greater  the  quantity  of  air  we  supply  to  the  furnace,  over 
and  above  that  actually  required  for  combustion,  the 
greater  will  be  the  loss  of  heat  due  to  the  temperature  of 
the  escaping  gases.  Again,  the  greater  the  quantity  of 
air  supplied  per  pound  of  coal  burned  the  larger  must  be 
the  chimney  to  carry  off  the  gases  from  the  furnace. 

It  is  evident,  therefore,  that  the  amount  of  air  supplied 
to  the  furnace  should  be  no  more  than  the  quantity  act- 
ually necessary  for  proper  combustion. 

71.  RATE  OF  COMBUSTION. —  By  the  rate  of  combustion 
is  meant  the  number  of  pounds  of  fuel  that  is  burned  per 
square  foot  of  grate  surface  per  hour. 

There  are  two  limits  to  the  rate  of  combustion,  a  max- 
imum and  a  minimum. 

The  maximum  rate  depends  upon  the  kind  of  fuel  and 
the  force  of  the  draft ;  and  where  the  draft  is  great  enough 
to  supply  the  amount  of  air  required  for  combustion,  the 


HEAT  AND  COMBUSTION  OF  FUEL.         169 

maximum  limit  will  be  reached  only  when  the  draft  be- 
comes so  great  as  to  blow  the  fuel  off  of  the  grate  bars. 
It  is  evident  that  this  limit  will  depend  somewhat  upon 
the  density  of  the  fuel.  It  is  probable  that  the  greatest 
rate  of  combustion  has  been  attained  in  locomotives, 
where  a  rate  of  about  120  pounds  of  anthracite  coal  has 
been  reached.  Of  course,  this  is  not  a  rate  that  is  con- 
tinued for  any  great  length  of  time. 

The  minimum  rate  of  combustion  depends  upon  the 
kind  and  nature  of  the  fuel  and  the  construction  of  the 
grate  of  the  furnace ;  it  is  the  rate  at  which  it  is  possible 
to  keep  a  bright  clear  fire  just  on  the  point  of  burning 
through  in  places,  and  so  admitting  a  body  of  cool  air  to 
chill  the  furnace.  For  anthracite  coal,  the  minimum  rate 
of  combustion  in  boiler  furnaces  is  about  4  pounds  ;  and 
for  bituminous  coal,  it  is  about  10  pounds. 

The  rate  of  combustion,  with  chimney  draft,  for  an- 
thracite coal,  will  vary  from  7  to  20  pounds,  the  average 
being  about  12  pounds;  for  bituminous  coal,  the  rate  will 
vary  from  12  to  40  pounds,  the  average  being  about  20 
pounds. 

The  whole  tendency  of  modern  practice  is  towards 
forced  draft  and  high  rates  of  combustion. 

72.  THE  FURNACE. —  In  Fig.  67  the  furnace  under  the 
boiler  is  shown  in  section.  It  will  be  seen  that  the  "  grate 
bars  "  rest  on  the  "  bridge  wall  "  at  the  back  end,  and  on 
the  "  dead  plate  "  at  the  front  end.  Where  the  grate  is 
long,  it  is  customary  to  make  it  up  of  two  lengths  of 
"  grate  bars  "  supported  at  the  middle  by  a  "  bearing 
bar." 

The  grate  bars  are  made  of  cast  iron  and  of  different 
shapes  for  different  kinds  of  fuels.  There  are  quite  a 
number  of  patented  grate  bars  on  the  market,  for  each  of 
ivhich  the  inventor  claims  certain  advantages. 

In  Fig.  68  is  shown  a  view  of  a  common  form  of  grate 


170 


STEAM   ENGINES    AND    BOILERS. 


bar.  The  bars  are  made  single  or  double,  in  order  that, 
by  using  a  number  of  single  and  double  bars,  grates  of 
any  desired  width  may  be  built  up.  There  are  lugs, 
marked  A  in  Fig.  68,  which  prevent  the  bars  from  being 


Fig.  68. 

packed  too  close  together,  and  which  cause  the  formation 
of  air  spaces,  through  which  the  air  for  combustion  enters 
from  the  "  ash-pit."  The  area  of  the  openings  for  the 
admission  of  air  between  the  grate  bars,  ought  to  be  made 
to  depend,  somewhat,  upon  the  kind  of  coal  burned,  but 
is  usually  about  one-half  the  total  area  of  the  grate. 

Where  very  fine  coal  is  used  the  area  of  the  openings 
should  be  less  than  where  coarser  coal  is  burned,  in  order 
that  there  may  not  be  a  great  waste  by  the  dropping  of 
coal,  through  the  openings,  into  the  ash-pit. 

In  Fig.  69  is  shown  a  somewhat  different  style  of  grate 
bar  that  is  quite  extensively  used. 

The  grate  bars  are  seldom  made  longer  than  four  feet ; 
and  grates  are  seldom  made  longer,  measured  from  the 


Fig.  69. 

furnace  door  to  the  bridge  wall,  than  seven  feet.  If  a 
grate  is  longer  than  seven  feet  it  becomes  almost  impos- 
sible to  fire  and  stoke  it  properly,  and  the  end  next  to  the 
bridge  is  very  apt  to  be  useless,  if  not  detrimental.  The 
grate  is  usually  built  with  a  slope,  from  the  front  of  the 


HEAT    AND    COMBUSTION    OF   FUEL.  171 

furnace  towards  the  bridge  wall,  of  from  one-half  to  one 
inch  fall  for  every  foot  in  length. 

The  dead-plate  at  the  front  of  the  grate  is  sometimes 
made  quite  large,  although  it  is  usually  rather  small. 

The  doors  of  the  furnace  should  be  made  double,  and 
should  have  perforations  in  them.  The  perforations  are 
for  the  admission  of  air,  which  aids  in  the  combustion  of 
the  gases  passing  off  from  the  fuel  on  the  grate  and, 
also,  cools  the  door  and  prevents  it  from  burning  out. 
The  inner  part,  or  lining,  of  the  door  is  to  prevent  the 
outer  part,  or  door  proper,  from  being  too  highly  heated 
by  the  heat  radiated  from  the  burning  fuel  on  the  grate. 

The  furnace  shown  in  Fig.  67  is  what  is  termed  an 
external  furnace,  since  it  is  exterior  to  the  boiler.  Some- 
times, however,  the  furnace  is  contained  in  the  boiler 
itself,  as  shown  in  Fig.  73,  when  it  is  termed  an  internal 
furnace. 

73.  FIRING  THE  FURNACE. —  The  term  "firing"  is 
applied  to  the  work  of  putting  the  fuel  in  the  furnace,  and 
keeping  the  fire  in  a  clean,  bright  condition.  To  the 
uninitiated  it  would  seem  as  if  the  whole  thing  to  be  done, 
in  feeding  a  furnace,  would  be  to  open  the  furnace  door 
and  throw  the  fuel  in  on  the  grate  ;  it  has  been  found, 
however,  that  in  order  to  preserve  a  good,  hot,  fire,  it  is 
best  to  adopt  some  system  of  firing. 

There  are  three  systems  in  common  use,  each  of  which 
has  its  advocates.  These  systems  are,  the  spreading,  the 
alternate,  and  the  coking. 

In  the  spreading  system,  the  fresh  charge  of  coal  is 
spread  in  a  layer  over  the  whole  area  of  the  grate.  This 
is  perhaps  the  most  common  system,  and  if  the  fire  is  fed 
frequently,  with  small  quantities  of  fresh  fuel  at  each 
charge,  it  will  give  good  results.  If,  however,  the  fire  is  fed 
at  rather  long  intervals,  with  a  large  quantity  of  fuel  at  each 
charge,  the  fire  will  be  chilled  every  time  fresh  fuel  is  put 


172  STEAM   ENGINES    AND    BOILERS. 

on  it.  This  chilling  of  the  fire  will  result  in  the  incom- 
plete combustion  of  the  gases  in  the  furnace  and  a  loss  of 
heat. 

The  alternate  system  can  only  be  used  to  advantage 
with  a  wide  grate.  In  this  system,  the  fresh  fuel  is  put 
alternately  on  each  side  of  the  grate  in  sufficient  quanti- 
ties to  cover  about  one-half  of  the  whole  surface.  The 
whole  area  of  the  grate  is  never  covered,  at  any  one  time, 
with  fresh  fuel ;  so  that,  the  whole  fire  is  never  chilled. 
The  gases  that  pass  off  from  the  fresh  fuel  on  one  side  of 
the  grate,  come  in  contact  with  the  surplus  hot  air  coming 
through  that  side  of  the  grate  on  which  there  is  no  fresh 
fuel,  and  are  burned.  This  system  of  firing  does  not  re- 
quire such  care  and  watchfulness  on  the  part  of  the  fire- 
man, as  does  the  spreading  system,  but  as  has  been  said, 
it  can  be  used  to  advantage  only  in  the  case  of  rather 
broad  furnaces. 

The  coking  system  is  the  system  that  has  been  adopted 
in  all  mechanical  stoking  devices.  In  it,  the  fresh  charge 
of  fuel  is  put  just  inside  the  door  of  the  furnace,  on  the 
dead  plate,  and  allowed  to  remain  there  until  the  greater 
part  of  the  most  volatile  gases  are  driven  off;  then  the 
coal  is  pushed  farther  back  into  the  furnace,  where  a  part 
of  it  is  burned  and  all  of  the  gases  are  driven  off,  and  a 
fresh  charge  is  put  on  the  dead  plate.  Each  succeeding 
charge  pushes  the  charges  preceding  it  further  towards 
the  end  of  the  furnace,  and  the  charges  are  put  in  at  such 
intervals  that  each  will  be  completely  burned  during  its 
passage  from  the  dead  plate  to  the  bridge  wall.  The 
gases,  evolved  from  the  charge  on  the  dead  plate,  are 
obliged  to  pass  over  the  hot  bed  of  fire  and  come  in  con- 
tact with  the  surplus  air  coming  through  the  back  end  of 
the  grate ;  and,  as  both  the  gases  and  the  air  are  at  a  high 
temperature,  there  is  a  strong  probability  that  all  the 
gases  will  be  burned.  This  method  of  firing  works 
equally  well  with  bituminous  coal  and  anthracite  coal, 


HEAT  AND  COMBUSTION  OF  FUEL, 


173 


174  STEAM    ENGINES    AND    BOILERS. 

but  is  of  more  value  where  bituminous  coal  is  used,  on 
account  of  the  large  per  cent  of  volatile  gases  such  coal 
contains. 

It  is  impossible  to  say  that  anyone  of  the  three  systems 
of  firing  is  better  than  another;  anyone  will  give  good 
results  if  it  is  properly  carried  out,  and  any  one  is  better 
than  no  system  at  all.  To  get  good  results  as  to  evapora- 
tion and  rate  of  combustion,  it  is  absolutely  necessary 
that  care  be  exercised  in  the  firing;  good  results  cannot 
be  obtained  by  careless,  bad  firing,  where  the  coal  is 
thrown  into  the  furnace  in  any  way  and  in  large  quanti- 
ties at  a  time. 

The  fire  should  be  kept  bright,  and  free  from  dirt  and 
clinkers,  and  of  as  nearly  a  uniform  thickness  over  the 
whole  grate  as  possible.  A  bright,  clean  fire  will  always 
give  better  results  than  one  that  is  dirty,  and  full  of 
clinkers  and  ash. 

The  thickness  of  the  bed  of  coals  has  quite  a  marked 
influence  upon  the  economy  of  the  combustion.  The 
best  thickness  will  depend  largely  upon  the  fuel  to  be 
burned,  but  it  may  safely  be  said  that  it  should  not  be 
allowed  to  be  less  than  six  inches  for  a  good,  hot  fire.  It 
is  seldom- that  the  thickness  of  the  fire  is  allowed  to  be 
greater  than  twelve  inches.  Experiments,  with  the  same 
coal,  have  shown  that  a  fire  six  inches  thick  gave  poorer 
results,  as  to  evaporation,  than  a  nine-inch  fire ;  and  the 
nine-inch  fire  gave  poorer  results  than  a  twelve-inch  fire. 
Care  should  be  taken  to  see  that  the  fire  never  burns 
through  in  spots,  leaving  a  portion  of  tne  grate  uncovered 
by  hot  coals. 

74.  MECHANICAL  STOKERS. —  There  are  several  forms 
of  mechanical  stokers  on  the  market,  and  almost  all -of 
them  feed  the  coal,  from  a  hopper,  onto  the  front  part  of 
the  furnace,  where  it  is  partially  burned,  and  from  where 
it  is  gradually  .made  to  move  back  along  the  grate  to  the 


HEAT  AND  COMBUSTION  OF  FUEL.         175 

bridge  wall.  The  rate  of  feeding  of  the  fuel  and  the  rate 
of  combustion  must  be  such  that  all  of  the  coal  will  be 
burned  on  its  way  from  the  furnace  door  to-  the  bridge 
wall.  If  the  rate  of  feeding  is  too  great,  the  fuel  will  not 
be  completely  burned  when  it  reaches  the  end  of  the 
grate,  and  a  part  of  it  will  be  forced  into  the  ash  pit,  and 
be  lost ;  while  if  the  rate  of  feeding  be  too  small,  the  part 
of  the  grate  next  to  the  bridge  wall  will  not  be  completely 
covered  with  live  coals,  and  cold  air  will  leak  through 
and  chill  the  gases  on  their  way  to  the  chimney. 

The  grates  of  almost  all  mechanical  stokers  are  usually 
inclined  at  a  considerable  angle  to  the  horizon,  and  the 
coal  is  made  to  move  from  the  dead-plate/to  the  bridge 
wall  by  a  movement  of  the  grate  bars.  This  movement 
is  generally  derived  from  a  shaft  that  is  rotated  by  a  s\nall 
engine. 

It  is  probable  that  the  Roney  Mechanical  Stoker  is.  one 
of  the  most  used  and  best  known  mechanical  stokers  in 
this  country.  Fig.  70  shows  the  Roney  Mechanical 
Stoker  as  applied  to  the  ordinary  return  tubular  boiler. 
In  Fig.  71  is  shown  the  stoker  in  detail. 

Referring  to  Fig.  71,  it  is  seen  that  the  grate  is  inclined 
from  the  front  of  the  furnace  towards  the  bridge  wall  ;,and 
that  the  grate  bars  are  arranged  as  steps,  with  their 
lengths  at  right  angles  to  the  direction  of  the  length  of 
the  boiler.  The  coal  is  fed  into  the  "coal  hopper,". and 
from  there  is  pushed  onto  the  "dead  plate ;"  the^coal  falls 
onto  the  front  grate  bars  and  is  made  to  move  from  one 
grate  bar  to  another,  towards  the  bridge  wall,  by  an  oscil- 
lating motion  of  the  grate  bars.  This  motion  of  the  grate 
bars  is  derived  from  the  "  rocker  bar,"  which  is  moved 
back  and  forth  by  the  "  connecting  rod. '  The  "  connect- 
ing rod  "  derives  its  motion  from  the  "  agitator,"  that  is 
connected,  by  means  of  the  "link,"  to  the  "disk-crank." 
The  disk-crank  is  rotated  by  the  shaft  to  which  it  is  fast- 
ened. By  the  motion  of  the  rocker  arm  the  grate  bars 


176 


STEAM   ENGINES    AND    BOILERS. 


HEAT    AND    COMBUSTION    OF    FUEL.  177 

are  made  to  assume  an  inclined  position,  and  then  a  stepped 
position.  When  the  bars  are  in  the  inclined  position,  the 
coal  tends  to  slide  down  the  grate  towards  the  bridge  wall. 
When  the  agitator  is  moved  out  towards  the  end  of  its  stroke 
it  strikes  a  nut  on  the  end  of  the  connecting  rod  and 
moves  the  rod  until  the  grate  bars  assume  the  inclined 
position.  As  the  agitator  moves  inward,  it  pushes  on  the 
pusher  and  forces  coal  from  the  hopper  onto  the  grate  and, 
also,  forces  the  coal  on  the  grate  down  the  grate  bars, 
which  remain  in  their  inclined  position  until  the  agitator 
strikes  the  inside  nut  on  the  connecting  rod.  Thus,  it  is 
seen  that  during  about  half  the  time  of  one  revolution  of 
the  disk  crank,  the  coal  on  the  grate  may  move  towards 
the  bridge,  and  during  the  other  half  of  the  time  it  is  at 
rest  on  the  grate.  By  means  of  the  "  feed  wheel/'  the 
pusher  may  be  adjusted  so  that  it  will  be  moved  forward 
during  any  desired  part  of  the  forward  motion  of  the 
agitator.  The  amount  of  coal  fed  to  the  furnace  depends 
largely  upon  the  adjustment  of  the  pusher,  although  in 
some  cases  the  weight  of  the  coal,  in  the  hopper  and  on 
the  grate,  will  cause  a  movement  of  the  coal  along  the 
grate.  By  adjusting  the  leek  nuts  on  the  connecting  rod, 
the  movement  of  the  grate  bars  may  be  adjusted.  Also, 
everything  may  be  made  to  occur  quicker  or  slower  by 
running  the  disk  crank  at  a  high  or  low  speed. 

75.  HAWLEY  DOWN  DRAFT  FURNACE. —  One  of  the 
latest,  successful,  improvements  in  furnaces  for  boilers 
may  be  said  to  be  the  down  draft  system  of  the  Hawley 
Down  Draft  Furnace  Co.  In  this  system,  two  grates  are 
used,  one  above  the  other,  as  shown  in  Fig.  72. 

The  upper  grate  is  made  up  of  a  number  of  tubes,  C, 
connected  to  the  drums  A  and  B.  The  drums,  A  and  B, 
are  connected  to  the  boiler,  so  that  there  is  always  a 
circulation  of  water  through  the  drums  and  through  the 
tubes.  The  bottom  grate,  Dy  is  of  the  ordinary  kind. 

12 


178 


STEAM    ENGINES    AND    BOILERS. 


/     l\    I     V 
i      \        ^ 

Id  X     \  /- ; 


/\ 


SB 


HEAT  AND  COMBUSTION  OF  FUEL.         179 

All  the  fresh  fuel  is  put  on  the  upper  grate,  through 
the  doors  F,  and  air  is  admitted,  also  through  Ft  over  the 
fuel.  By  the  arrangement  of  the  furnace,  the  air  and 
gases  of  combustion  are  made  to  pass  down  through  the 
upper  grate  in  order  to  reach  the  chimney.  All  the  fine 
particles  of  coal,  and  partially  burned  coal,  drop  between 
the  upper  grate  bars  and  fall  onto  the  lower  grate  ;  so  that, 
the  lower  grate  is  always  covered  with  a  thick  layer  of 
hot  coals.  Air  is  admitted  through  the  ash  pit,  and  it 
passes  up  through  the  hot  coals  on  the  lower  grate  ;  a 
part  of  this  air  is  used  in  burning  the  coals  on  the  lower 
grate ;  the  remainder  comes  in  contact  with  the  hot, 
combustible,  gases  from  the  upper  grate  and  burns  them. 

This  furnace  has  given  good  results  as  a  preventer  of 
smoke. 


CHAPTER     IX. 

BOILERS. 

76.  TYPES  OF  BOILERS. —  Before  considering  the  dif- 
ferent types,  it  will  be  well  to  define  certain  terms  used 
in  referring  to  boilers. 

The  grate  surface  is  the  area  of  the  grate  of  the  fur- 
nace of  the  boiler. 

The  heating  surface  is  the  area  of  the  surface  of  con- 
tact of  the  hot  gases  with  the  boiler,  while  on  their  way 
from  the  furnace  to  the  boiler  chimney. 

The  shell  is  the  main  vessel  in  which  is  contained  the 
water  and  steam. 

The  water  space  is  the  volume  of  that  part  of  the  boiler 
occupied  by  the  water. 

The  steam  space  is  the  volume  of  that  part  of  the  boiler 
occupied  by  the  steam. 

All  classifications  of  boilers  are  based,  generally,  upon 
peculiarities  in  the  design  of  the  shell,  or  in  the  relative 
position  of  the  heating  surface  and  grate  surface.  Boilers 
are,  also,  often  classified  according  to  the  place  where 
they  are  to  be  used.  Among  the  different  classifications 
may  be  mentioned  the  following:  marine  boilers,  land 
boilers ;  upright  boilers,  horizontal  boilers ;  internally  fired 
boilers,  externally  fired  boilers;  fire-tube  boilers,  water- 
tube  boilers. 

A  marine  boiler  is  one  that  is  used  on  vessels ;  and  a 
land  boiler  is  one  that  is  used  on  land. 

An  upright  boiler  is  one  having  the  axis  of  the  shell 
(180) 


BOILERS. 


181 


vertical ;  and  a  horizontal  boiler  is  one  having  the  axis  of 
the  shell  horizontal. 

An  internally  fired  boiler  is  one  that  has  its  furnace 
inside  the  shell  of  the  boiler ;  and  an  externally  fired 
boiler  is  one  that  has  its  furnace  exterior  to  the  shell. 

A  fire-tube  boiler  is  one  a  part  of  whose  heating  sur- 
face is  the  internal  surfaces  of  a  number  of  tubes  sur- 
rounded by  water ;  and  a  water-tube  boiler  is  one  a  part 
of  whose  heating  surface  is  the  external  surfaces  of  a 
number  of  tubes  filled  with  water. 

77.  OLD  TYPES  OF  BOILERS. —  Under  this  head  has 
been  included  those  forms  of  boilers  that  were  first  used, 
and  that  are  still  used  to  a  large  extent  in  England,  but 


Fig.  73. 


that  are  seldom  met  with  in  this  country.  The  principal 
among  these  may  be  said  to  be  the  Cornish  boiler  and 
the  Lancashire  boiler. 

The  Cornish  boiler  is  an  internally  fired  boiler,  with  a 
cylindrical  shell.  The  furnace  is  contained  in  a  large 
cylindrical  flue  running  the  whole  length  of  the  boiler 
from  front  to  rear.  In  Fig.  73  is  shown  a  longitudinal 
section  of  a  Cornish  boiler,  and  in  Fig.  74  is  shown  a 


182 


STEAM    ENGINES    AND    BOILERS. 


cross-section  of  one.  The  furnace  is  in  the  flue  A,  and 
the  products  of  combustion  pass  through  A  to  the  rear  of 
the  boiler,  where  they  divide  into  two  portions,  and  return 
through  the  passages  B  to  the  front  of  the  boiler,  they 
then  enter  C  and  pass  through  it  to  the  chimney. 


Fig.  74. 

The  Cornish  boiler  has,  always,  but  a  single  furnace  and 
a  single  flue. 

The  Lancashire  boiler,  like  the  Cornish  boiler,  is  an 
internally  fired  boiler,  but  it  differs  from  the  Cornish 
boiler  in  having  two  furnaces  and,  for  a  part  of  its  length, 
two  flues.  The  two  flues  of  the  Lancashire  boiler  are 
united  into  a  single  flue  near  the  back  end  of  the  boiler. 
The  distinguishing  features  of  the  Lancashire  boiler  are 
the  two  furnaces  and  the  two  flues  uniting  in  the  single 
flue  a  short  distance  from  the  back  end  of  the  boiler. 

The  Cornish  and  Lancashire  boilers  built  to-day  are 
almost  always  provided  with  "  Galloway  tubes  "  across  the 
flues.  These  are  shown  in  Fig.  75,  and  are  simply  tubes, 
a,  of  the  shape  of  a  truncated  cone,  placed  in  an  inclined 


BOILERS. 


183 


position  across  the  large  flue  b.  They  facilitate  the  cir- 
culation of  the  water  in  the  boiler  and  increase  the  heating 
surface. 

In   many  of  the   modern   forms  of  Cornish   or  Lanca- 
shire boilers,  the  gases  pass  under  the  boiler  from    the 


Fig.  75. 

rear  towards  the  front,  instead  of  along  the  sides,  and 
pass  along  the  sides  on  the  way  to  the  chimney.  That 
is,  in  Figs.  73  and  74,  the  gases  pass  to  the  front  through 
the  passage  C,  after  leaving  A,  and  then  pass  off  to  the 
chimney  through  the  passages  B. 

78.  RETURN  FIRE-TUBE  BOILERS. —  Boilers  of  this 
type  are  usually  spoken  of  as  "  return  tubular  boilers," 
and  are  more  used  in  this  country  than  those  of  any  other 
type. 

In  Figs.  67  and  76  are  shown  views  of  a  boiler  of  this 
type. 

These  boilers,  as  seen  from  the  cuts  shown,  are  cylin- 
drical, externally  fired,  boilers.  The  gases  pass  from  the 
furnace  under  the  boiler  to  the  '*  back  connection,"  and 


184 


STEAM    ENGINES    AND    BOILERS. 


^BOILERS. 


185 


from  there  pass  to  the  front  through  a  number  of  tubes 
or  flues.  If  the  tubes  are  of  greater  diameter  than  six 
inches,  they  are  usually  spoken  of  as  flues.  The  number 
of  tubes  varies  with  the  diameter  of  the  shell  of  the 
boiler  and  the  diameter  of  the  tubes. 

The  heating  surface  of  a  return  tubular  boiler  consists 
of  that  part  of  the  surface  of  the  shell  in  contact  with 
the  gases ;  of  the  outside  surface  of  the  tubes,  the  surface 
in  contact  with  the  water ;  and  that  part  of  the  ends, 
or  heads,  of  the  boiler  with  which  the  gases  come  in 
contact.  The  area  of  the  surface  of  the  shell  that  is  in 


I 

Fig.  77. 

contact  with  the  gases  depends  upon  the  setting  of  the 
boiler;  although  it  is  customary  to  assume,  what  is  not 
always  true,  that  two-thirds  of  the  area  of  the  shell  is 
exposed  to  the  hot  gases.  It  is  usually  customary  to 
neglect,  as  unimportant,  the  parts  of  the  heads  in  contact 
with  the  gases.  It  is  evident,  then,  that  the  heating  sur- 
face of  the  shell  will  be  obtained  by  multiplying  two- 
thirds  the  outside  circumference  of  the  shell,  in  feet, 
by  the  length,  in  feet ;  and  the  heating  surface  of  the 
tubes  will  be  obtained  by  multiplying  the  outside  cylin- 
drical surface  of  one  tube  by  the  number  of  tubes  in 


186 


STEAM    ENGINES    AND    BOILERS. 


BOILERS. 


187 


the  boiler.  Therefore,  let  D  denote  the  diameter,  in 
feet,  of  the  shell  of  the  boiler;  /,  the  length  in 
feet ;  d,  the  outride  diameter,  in  inches,  of  each  tube  ; 
and  N,  the  number  of  tubes.  Then  the  heating 

2 

surface   of  the   shell  will    be,     3.1416  X  --  Dl ;  and  that 

*J 


Fig.  79. 


Fig.  80. 


3.14.16  dlN 

of  the  tubes  will  be — .     The  total    heating  sur- 
face, S,  will  be 

(83) 


=  2.1  Dl  +  0.262  dlN. 


The  tubes  used  in  return  tubular  boilers  are  sold  accord- 
ing to  their  external  diameter;  and  the  diameters  in  most 


188 


STEAM   ENGINES    AND   BOILERS. 


00 

bfl 


BOILERS.  189 

common  use  are  3,  3^,  and  4  inches.  The  diameter  of 
the  tube  used  in  a  boiler  is  somewhat  limited  by  its 
length,  as  the  length  should  not  exceed  sixty  times  the 
diameter. 

The  diameters  of  the  shells  of  return  tubular  boil- 
ers vary  from  about  30  inches  to  84  inches;  and  the 
lengths  of  the  shells  will  vary  from  about  6  feet  to  20 
feet,  although  the  usual  lengths  are  from  12  to  16  feet. 

Boilers  whose  diameters  do  not  exceed  72  inches,  and 
whose  lengths  are  not  greater  than  18  feet,  may  be 
obtained  with  the  bottom  of  the  shell  made  of  a  single 
sheet  of  iron  or  steel,  and  the  top  part  made  of  one  or 
more  sheets.  The  advantage  of  a  single  sheet  on  the 
bottom  of  an  externally  fired  boiler,  is  that  there  are  then 
no  rivets  to  come  in  contact  with  the  hot  gases. 

The  ends  of  tubes  less  than  six  inches  in  diameter 
are  fastened  in  the  heads  of  the  boilers  by  "  expanding" 
them,  as  shown  in  Fig.  77,  and  those  six  inches,  or  more, 
in  diameter  are  riveted  to  the  heads. 

79.  WATER-TUBE  BOILERS.  —  Boilers  of  this  type  are 
not  as  much  used  as  those  of  the  return  fire-tube  type, 
but  they  are  becoming  more  and  more  extensively  used 
every  day.  The  first  cost  of  these  boilers  is  usually  much 
greater  than  that  of  boilers  of  other  types.  The  heating 
surface  of  these  boilers  is  made  up  of  such  a  variety  of 
surfaces  that  it  is  impossible  to  give  any  general  rule  for 
determining  it,  that  will  be  applicable  to  all  kinds  of 
water-tube  boilers.  It  must  suffice  to  say  that  the  heat- 
ing surface  is  the  total  surface  of  those  parts  of  the  boiler 
in  contact  with  the  hot  gases. 

It  is  impossible  to  illustrate  and  explain  all  the  different 
varieties  of  water-tube  boilers,  but  they  may  be  distin- 
guished into  three  classes,  each  of  which  may  be  illus- 
trated. 


190 


STEAM    ENGINES    AND    BOILERS. 


*\£jfcv.5 .*..  £•    S_ 

mi 


tc 


BOILERS.  191 

In  the  first  class  are  included  those  water-tube  boilers 
that  have  a  number  of  tubes  fastened  together  into  sets 
by  common  headers  or  legs,  and  these  common  headers 
connected 'to  a  drum  containing  water  and  steam.  The 
form  of  the  headers,  connecting  the  ends  of  the  tubes, 
depends  upon  the  make  of  the  boiler  and  the  number  of 
tubes  connected  into  one  set.  From  all  boilers  of  this 
class,  it  is  possible  to  remove  one  set  of  tubes  without 
in  any  way  injuring  the  other  sets.  It  is  probable  that  the 
greater  number  of  all  the  water-tube  boilers  on  the  market 
belong  to  this  class. 

As  an  example  of  this  class  of  water-tube  boilers,  the 
Babcock  and  Wilcox  boiler  is  shown. 

Fig.  78  shows  a  section  of  this  boiler;  Fig.  79  shows  an 
enlarged  view  of  the  connection  of  the  tubes  to  the  head- 
ers, and  of  the  connection  of  the  headers  to  the  water  and 
steam  drum.  In  Fig.  80  is  shown  a  front  view  of  one  of 
the  headers.  It  will  be  seen  that  each  header,  both  at 
the  front  and  the  rear,  is  entirely  independent  of  the 
others,  and  that  by  taking  off  the  hand-hole  covers,  a  in 
Figs.  79  and  80,  one  of  which  is  placed  on  the  headers 
opposite  the  end  of  each  tube,  the  tubes  may  be  exam- 
ined, or  taken  out  if  desired. 

In  some  forms  of  water-tube  boilers,  of  this  class,  the 
headers  are  so  arranged  that  the  water  from  the  lower 
tubes  must  flow  through  the  headers  of  the  upper  tubes 
before  it  can  enter  the  water  and  steam  drum. 

The  Heine  boiler  will  serve  to  illustrate  what  might  be 
termed  the  second  class.  In  this  class  would  be  included 
all  those  water-tube  boilers  that  have  the  ends  of  all  the 
tubes  fastened  into  one  common  header  at  each  end  of 
the  boiler. 

Fig.  8 1  shows  a  perspective  of  a  Heine  boiler  ready 
for  shipment ;  Fig.  82  shows  a  section;  and  Fig.  83  shows 
the  method  of  fastening  the  tubes  to  the  header,  and  the 


192 


STEAM    ENGINES    AND    BOILERS. 


details  of  the  hand  holes,  one  of  which  is  placed  opposite 
the  end  of  each  tube.  In  Fig.  83,  T  represents  the  ends 
of  the  tubes  fastened  to  the  header;  0,  hollow  stay-bolts 
bracing  the  walls  of  the  header;  and  Jt  h,  Ht  and  b,  parts 
of  the  hand-hole  cover. 

In  the  third  class  of  water-tube  boilers,  would  be 
included  those  that  have  two  or  more  large  drums  con- 
nected by  nearly  vertical  water-tubes. 


Fig.  83. 

This  class  is  illustrated  by  the  Stirling  boiler;  a  section 
of  which  is  shown  in  Fig.  84,  and  a  half-front  elevation 
in  Fig.  85. 


80.  VERTICAL  BOILERS. —  Until  of  late  years  almost  all 
vertical  boilers  made  were  of  small  size,  but  now  large 
ones  are  being  made  and  used.  These  boilers  are  usually 
what  might  be  termed  internally  fired  ;  and  they  are  liked 
on  account  of  the  small  floor  area  occupied  by  them. 

In  Fig.  86  is  shown  a  half-section  and  half-elevation  of 
a  small  vertical  boiler,  such  as  is  in  common  use  in  this 
country. 

The  heating  surface  in  these  boilers  consists  of  the  sur- 


BOILERS. 


193 


Fi«.  84. 
Stirling  Boiler, 


13 


194  STEAM    ENGINES    AND    BOILERS. 

face  of  the  furnace  and  of  the  outside  surface  of  the  tubes 
through  which  the  gases  pass.  The  tubes  of  these  small, 
vertical  boilers  are  usually  of  2  or  2j  inches  outside 
diameter. 

81.  MARINE    BOILERS. —  While    any    boiler  used  on  a 
vessel  is,  or  ought  to  be,  called  a  "  marine  boiler/'  custom 
has  generally  confined  the  name  to  boilers  similar  to  that 
show  in  section  in  Fig.  87,  and  in  half-elevation  and  half- 
section  in  Fig.  88. 

These  boilers  are  always  internally  fired  ;  they  make 
steam  rapidly  and  occupy  but  a  small  amount  of  space. 
The  tubes  used  in  marine  boilers  are  usually  about  2j 
inches  in  external  diameter. 

82.  RATING  OF    BOILERS. —  Most   boilers   are    usually 
rated    as    being    of    a    given    number   of    horse-power. 
By  the   term  horse-power,  when  applied  to  a  boiler,  is 
meant  the  horse-power  of  the  engine  to  which  the  boiler 
is    capable    of  supplying  steam.     Of  course,  it  is  at  once 
evident  that  the  power  of  a  boiler  will  vary  between  very 
wide  limits,  depending  upon  the  efficiency  in  the  use   of 
steam  of  the  engine  to  which  it  is  attached. 

In  order  that  there  might  be  some  uniformity  in  the 
rating  of  the  boilers  tested  at  the  Centennial  Exposition, 
at  Philadelphia,  in  1876,  the  judges  decided  that  one 
boiler  horse-power  should  mean  thirty  pounds  of  water 
per  hour,  evaporated  from  an  initial  temperature  of  100° 
F.,  under  a  boiler  pressure  of  seventy  pounds  by  the 
gauge.  This  is  equal  to  34^  Ibs.,  per  hour,  of  equivalent 
water  from  and  at  212°.  This  standard  of  rating  has 
become  almost  universally  adopted,  and  one  horse-power 
for  a  boiler  may  be  considered  as  the  evaporation  of  34  J 
pounds  of  water  per  hour  from  and  at  212°,  or  its 
equivalent.* 

*  This  has  been  adopted  as  the  standard  boiler  horse-power  by  the  American 
Society  of  Mechanical  Engineers. 


BOILERS. 


195 


Fig.  85 
Stirling  Boiler. 


196  STEAM    ENGINES    AND    BOILERS. 

When,  however,  boilers  are  sold  and  no  test  is  made  to 
determine  the  amount  of  steam  they  will  make,  they 
cannot  be  rated  according  to  the  standard  of  34^  pounds 
of  water  per  hour  from  and  at  212°;  and  manufacturers 
usually  rate  them  according  to  the  number  of  square  feet 
of  heating  surface.  There  is  no  uniformity  among  manu- 
facturers as  to  the  number  of  square  feet  of  heating 
surface  that  shall  be  necessary  for  one  horse-power,  nor 
is  any  distinction  made  as  to  the  difference  in  efficiency 
of  the  different  parts  of  the  heating  surface.  Some 
manufacturers  of  return  tubular  boilers  rate  their  boilers 
on  the  basis  of  I2j  square  feet  of  heating  surface  per 
horse-power,  while  others  rate  their  boilers  on  a  basis  of 
15  square  feet  of  heating  surface  per  horse-power. 

Manufacturers  of  water-tube  boilers  usually  rate  their 
boilers  on  a  basis  of  10  or  n  square  feet  of  heating  sur- 
face per  horse-power. 

Vertical  boilers  are  usually  rated  upon  a  basis  of  12 
square  feet  of  heating  surface  per  horse-power. 

When  comparing  the  prices  asked  by  different  manu- 
facturers for  boilers  of  the  same  rated  horse-power,  it  is 
necessary  to  compare  carefully  the  areas  of  the  heating 
surfaces,  in  order  to  determine  whether  or  not  the  boilers 
are  rated  on  the  same  basis. 

83.  APPENDAGES  TO  A  BOILER. —  Under  this  head  are 
included  pressure  gauges,  water  gauges,  gauge  cocks, 
safety  valves,  feed-water  heaters,  and  other  small  parts  of 
a  boiler  that  need  some  short  description. 

Pressure  Gauges. —  The  most  common  form  of  pressure 
gauge  is  shown  in  Figs.  89  and  90.  In  Fig.  90  the  pres- 
sure gauge  is  indicated  by  a.  It  has  a  dial  face  graduated 
to  show  pressure  in  pounds  per  square  inch  above  the 
atmosphere,  so  that  when  the  pressure  in  the  boiler  is 
simply  that  of  the  atmosphere  the  gauge  will  indicate  zero 
pounds.  Fig.  89  shows  a  pressure  gauge  with  the  dial 


BOILERS. 


197 


Fig.  86.     Vertical  Boiler. 


198 


STEAM    ENGINES    AND    BOILERS. 


face  removed,  so  that  the  inside  mechanism  can  be  seen. 
The  steam  enters,  through  #,  the  flexible,  bent  tube  b, 
shown  in  section  at  ey  and  by  its  pressure  tends  to 
straighten  the  tube.  As  the  tube  straightens,  it  moves  the 
arc  c ;  which  in  turn  moves  the  hand  d  by  means  of  a 


Fig.  87. 
Marine  Boiler. 

small  pinion  fastened  to  the  axis  of  d  and  gearing 
with  c.  By  properly  adjusting  the  position  the  hand  dy 
and  the  strength  of  the  tube  /5,  the  gauge  may  be  made 
to  correctly  indicate  pressures. 

Syphon. —  The  syphon  is  simply,  a  bent  piece  of  J 
inch  pipe,  shown  at  b  in  Fig.  90,  to  which  the  gauge  is 
always  fastened.  The  syphon  is  used  in  order  to  keep 
the  tube  of  the  pressure  gauge  filled  with  water,  and  thus 


BOILERS. 


199 


t 


200  STEAM    ENGINES    AND    BOILERS. 

prevent  the  very  hot  steam  from  coming  in  direct  contact 
with  it. 

Water  Column. —  The  water  column  is  a  casting  to 
which  is  fastened  a  number  of  the  small  appendages  to  a 
boiler.  In  Fig.  90,  A  indicates  the  water  column.  To  it 
is  fastened  the  pressure  gauge  a,  the  gauge  cocks  c,  and 
the  water  gauge  d.  The  upper  part  of  A  is  connected 
to  the  steam  space  of  the  boiler,  and  the  lower  part  to  the 
water  space;  so  that  the  water  stands  at  the  same  level 
in  the  water  column  that  it  does  in  the  boiler. 

Gauge  Cocks. —  The  gauge  cocks  c,  in  Fig.  90,  are  for 
determining  the  position  of  the  water  line  in  the  boiler. 
There  are  usually  three  gauge  cocks,  about  three  inches 
apart.  The  water  line  should  be  just  about  the  middle 
cock,  so  that  if  the  upper  cock  is  opened,  steam  will 
escape;  if  the  middle  cock  is  opened, a  mixture  of  steam 
and  water  will  escape ;  and  if  the  lower  cock  is  opened, 
water  will  escape.  Boilers  are  sometimes  provided  with 
two  sets  of  gauge  cocks,  one  fastened  to  the  water 
column  and  one  fastened  directly  to  the  shell  of  the 
boiler. 

Water  Gauge. —  The  water  gauge  or,  as  it  is  sometimes 
called,  the  water  glass,  is  indicated  by  d,  in  Fig.  90.  It 
is  a  glass  tube  communicating  with  the  steam  space  of  A 
at  the  top,  and  with  the  water  space  at  the  bottom.  If 
the  tube  is  open  and  not  choked  at  any  point,  the  level 
of  the  water  in  the  water  gauge  will  be  the  same  as  that 
of  the  water  in  the  boiler ;  so  that  the  water  in  the  gauge 
will  enable  one  to  see  at  a  glance  where  the  level  of  the 
water  stands  in  the  boiler.  The  glass  tube  has,  usually, 
about  twelve  inches  exposed  to  view;  and  the  middle 
gauge  cock  is  at  about  the  middle  of  the  glass  tube. 
The  lower  end  of  the  glass  tube  is  about  on  the  level  of 
the  tops  of  the  tubes  of  the  boiler,  in  the  case  of  a  return 
fire-tube  boiler. 

Safety    Valve. —  A  safety  valve  is  a  valve  which,  when 


BOILERS. 


201 


Fig.  90. 


202 


STEAM    ENGINES    AND    BOILERS. 


the  pressure  of  the  steam  becomes  equal  to  a  given 
amount  depending  upon  the  setting  of  the  valve,  is  opened 
by  the  pressure  of  the  steam,  and  allows  some  of  the 
steam  to  " blow  off"  into  the  atmosphere;  it  thus  pre- 
vents the  pressure  in  the  boiler  from  becoming  too  great. 
There  should  be  at  least  one  safety  valve  on  every  boiler, 
and  it  is  desirable  to  have  two  safety  valves  to  every 
boiler,  in  order  that  if,  for  any  reason,  one  of  the  valves 
should  fail  to  act  the  other  would  act. 


Fig.  91. 

There  are  two  kinds  of  safety  valves  in  common  use  on 
boilers  generating  steam  for  steam  engines,  the  lever 
safety  valve  and  the  pop  safety  valve. 

In  Fig.  91  is  shown  a  lever  safety  valve.  It  consists  of 
a  valve,  in  the  body  A,  to  which  is  a  spindle  Bt  that 
presses  against  a  lever,  D.  The  lever  is  free  to  swing 
about  the  pin  C,  and  carries  a  poise,  W,  whose  position  on 
the  lever  may  be  changed  at  will.  The  steam  presses 


BOILERS. 


203 


against  the  bottom  of  the  valve,  in  the  body  A,  and  tends 
to  force  the  spindle,  B,  upwards.  In  order  that  the 
spindle  may  rise  and  allow  the  valve  to  open,  the  lever 
must  be  moved  about  the  pin,  C,  as  a  center;  but  the 
weight  of  the  lever,  Dt  and  the  poise,  W,  tends  to  keep 
the  lever  from  moving.  It  is  evident  that  the  valve  will 
not  open  until  the  moment  of  the  force  acting  on  the 
valve  becomes  equal  to  the  sum  of  the  moments  of  the 
weight  of  the  lever  and  the  weight  of  the  poise. 


Fig.  92. 


Let,  in  Fig.  91,  V  be  the  area  of  the  valve  in  square 
inches;  Pt  the  pressure  of  the  steam,  by  the  gauge,  at 
which  the  valve  will  blow  off;  a,  the  distance,  in  inches, 
from  the  center  of  Cto  the  center  of  the  spindle  B;  b,  the 
distance,  in  inches,  to  the  center  of  the  poise  ;  c,  the  dis- 
tance, in  inches,  to  the  center  of  gravity  of  the  lever;  wt 
the  weight,  in  pounds,  of  the  lever ;  W,  the  weight,  in 
pounds,  of  the  poise  ;  and  m,  the  weight,  in  pounds,  of 
the  valve. 


204  STEAM    ENGINES    AND    BOILERS. 

Then,  it  is  evident  from  Fig.  91,  that 

(84)  PVa  =  cw  +  b  W  -f  ma 

From  (84)  we  get 


In  a  given  safety  valve,  the  only  thing  that  can  be 
changed  is  the  distance,  b,  that  the  poise  is  from  the 
center  of  the  pin  C;  and  the  greater  b  is  made,  the  higher 
will  be  the  pressure  at  which  the  valve  will  blow  off. 

A  "  pop  "  safety  valve  is  a  safety  valve  in  which  the 
valve  is  held  down  on  its  seat  by  a  spring,  instead  of  a 
lever  and  poise.  In  Fig.  92  is  shown  a  section  of  a 
"  pop  "  safety  valve  such  as  is  manufactured  by  the  Con- 
solidated Safety  Valve  Co.  The  valve  is  set  to  blow  off 
at  different  pressures  by  adjusting  the  tension  of  the 
spring  by  means  of  the  nuts  at  the  top. 

The  only  objection  to  a  pop  safety-valve  is  the  noise  it 
makes  when  it  opens. 

Feed-  Water  Heater.  —  We  have  already  shown  how 
the  amount  of  heat  required  to  evaporate  a  pound  of 
water  is  reduced  by  increasing  the  temperature  of  the  feed 
water  before  it  enters  the  boiler.  Whenever  it  is  possible, 
the  exhaust  steam  of  a  non-condensing  engine  should  be 
used  to  heat  the  feed  -water,  instead  of  being  allowed  to 
pass  off  into  the  atmosphere.  The  apparatus  in  which 
the  feed-water  is  heated  before  entering  the  boiler  is 
termed  a  "  feed-water  heater." 

In  Fig.  93  is  shown  a  National  feed-water  heater. 
As  seen  in  the  cut,  the  feed-water  is  made  to  pass  through 
a  coil  of  pipe,  before  entering  the  boiler,  that  is  surrounded 
by  the  exhaust  steam. 

Sometimes  a  feed-water  heater  is  made  to  serve  the 
double  purpose  of  heating  the  feed-water,  and  of  catching 
all  the  sediment  and  impurities  that  would  otherwise  be 


BOILERS.  205 

deposited  in  the  boiler,  when  the  water  has  been  heated 
as  hot  as  it  becomes  in  the  heater. 

Feed  Pipe.  — The  feed  pipe  is  the  pipe  through  which 
the  water  enters  the  boiler.  It  is  often  attached  to  the 
shell  of  the  boiler  near  the  back,  or  to  the  bottom  of  the 
front  end.  Neither  of  these  positions,  however,  is  to  be 
recommended,  as  in  either  case  the  comparatively  cool 
feed-water  impinges  upon  the  hottest  part  of  the  shell. 


tXHA'JSt  flfE 


It  is  better  that  the  feed  pipe  should  be  attached  to  the 
front  end  of  the  boiler  a  few  inches  below  the  water  line, 
and  be  carried  back  into  the  boiler;  and  the  water  should 
be  allowed  to  escape  from  the  pipe  through  small  perfora- 
tions in  it,  rather  than  through  the  open  end. 

Bloiv-off  Pipe. —  Every  boiler  should  have  a  blow-off 
pipe,  by  means  of  which  it  may  be  emptied  of  the  water 
it  contains. 


206 


STEAM    ENGINES    AND    BOILERS, 


BOILERS.  207 

Valves. —  The  steam  pipe,  for  taking  steam  from  the 
boiler  to  the  engine,  should  have  a  valve  close  to  the 
boiler. 

The  feed  pipe  should  have  two  gate  valves,  close  to  the 
boiler,  with  a  check  valve  between  them. 

The  blow-off  pipe  should  not  have  a  valve  on  it,  but 
should  have  a  good  plug-cock. 

Feeding  Apparatus. —  The  feed-water  is  usually  forced 
into  the  boiler  by  means  of  a  pump,  called  a  feed-water 
pump,  although  the  injector  is  often  used. 

84.  SETTINGS  OF  BOILERS. —  The  setting  of  a  boiler 
means  the  general  arrangement  of  furnace,  boiler,  and 
chimney  relative  to  one  another,  and  the  manner  in  which 
the  furnace  and  boiler  are  inclosed  and  built  in.  Of 
course,  the  setting  will  depend  largely  upon  the  type  and 
construction  of  the  boiler,  but  for  the  ordinary  return 
fire-tube  boiler  there  are  two  recognized  standard  settings, 
viz.,  the  full-arch  front  setting,  and  the  half-arch  front 
setting. 

Fig,  76  shows  a  perspective  view  of  a  return  fire-tube 
boiler  with  a  half-arch  front  setting ;  and  Fig.  94  shows 
one  with  a  full-arch  front  setting. 

When  two  or  more  boilers  are  set  side  by  side,  with 
common  front  and  rear  walls,  they  form  what  is  termed  a 
"  battery  "  of  boilers.  All  the  boilers  of  a  battery  may, 
or  may  not  be  connected  to  the  same  chimney. 

The  setting  for  return  fire-tube  boilers,  recommended 
by  the  Hartford  Steam  Boiler  Inspection  and  Insurance 
Company,  described  in  The  Locomotive  for  February, 
1895,  is  shown  in  Figs.  95,  96  and  97. 

In  this  setting  the  furnace  is  supposed  to  be  lined  with 
fire-bricks,  and  the  walls  are  made  very  thick.  The 
company,  in  its  description  of  the  setting,  says:  — 

"  The  width  of  the  furnace  in  the  settings  advocated 
by  this  company  is  six  inches  less  than  the  diameter  of 


208 


STEA3I    ENGINES    AND     BOILERS. 


the  boiler.  Beginning  just  above  the  grate,  the  side  walls 
batter  at  such  angle  as  to  make  them  3"  clear  of  the 
boiler  at  the  center,  where  the  walls  project  inward  and 
close  against  the  boiler.  This  batter  gives  greater  sta- 
bility to  the  walls,  and  another  special  feature  of  it  is, 
that  it  allows  the  heated  gases  to  rise  without  impinging 
against  the  walls  of  the  setting,  and  they  flow  away  from 


Fig.  95. 

the  wall  and  distribute  themselves  evenly  over  the  whole 
heating  surface  of  the  shell.  The  removal  of  soot  and 
ash  from  the  shells  is  also  facilitated,  and,  moreover,  it  is 
found  that  these  deposits  do  not  form  so  readily  when  the 
walls  are  battered  as  they  do  when  the  walls  are  straight, 
and  the  space  between  them  is  correspondingly  con- 
tracted. The  batter  also  increases  the  volume  of  the 
combustion  chamber,  and  allows  of  a  more  thorough 
mixing  of  the  oxygen  and  furnace  gases,  the  result  being 
that  complete  combustion  of  the  fuel  is  greatly  facilitated. 
The  bridge-wall  slopes  back  from  about  four  inches  above 
the  grate,  at  an  angle  of  40°,  in  order  that  the  radiant 
heat  from  the  fire  may  be  diffused  over  a  large  portion 


BOILERS. 


209 


of  the  boiler  shell.  The  flame  bed  back  of  the  bridge- 
wall  slopes  down  to  the  level  of  the  boiler-room  floor. 
It  is  paved  for  easy  cleaning,  and  the  combustion  cham- 
ber is  large  enough  to  make  examinations  and  repairs  to 
the  boiler  comparatively  easy.  The  cleaning  door  in 
the  rear  wall  is  placed  on  a  level  with  the  flame  bed  in 
order  that  ashes  may  be  readily  removed,  and  as  it  is 


Fig.  96. 

below  the  currents  of  highly-heated  gases  loss  by  radia^ 
tion  through  the  door  is  largely  prevented.  The  loss  or 
waste  of  heat  from  this  cause  is  often  very  great  and  it 
has  not  generally  received  the  attention  it  deserves. 
Another  point  that  demands  more  attention  than  it 
usually  receives,  is  the  liability  of  leakage  of  cold  air 
through  the  walls  of  the  setting,  with  the  resulting  reduc- 
tion of  furnace  temperature.  To  avoid  loss  of  tempera- 
ture from  this  cause  heavy  double  walls  are  constructed 
in  this  company's  settings,  the  outside  walls  of  a  battery 
having  a  two-inch  air  space  between  them.  The  division 

H 


210 


STEAM    ENGINES    AND    BOILERS. 


walls  between  two  or  more  boilers  should  have  a  half-inch 
clear  space  between  them,  to  allow  free  and  independent 
expansion  of  the  walls.  With  a  solid  wall  and  one  or 
more  boilers  of  the  battery  stopped,  one  side  of  the  wall 
separating  a  boiler  in  use  from  another  one  out  of  use 
would  be  hot  and  greatly  expanded,  while  the  other  side 
of  it  would  be  cool ;  the  result  being  that  the  bonded  or 


Fig.  97. 


solid  wall  must  necessarily  be  severely  strained  or  injured, 
and  the  joints  in  the  masonry  quite  probably  broken  by 
the  unequal  expansion.  Excessive  leakage  of  air  is  likely 
to  follow.  These  criticisms  apply  to  all  solid-built  boiler 
settings.  While  the  heavy  double  walls  are  somewhat 
more  expensive  in  first  cost,  the  increased  economy  and 
capacity  of  the  boilers,  as  well  as  the  greater  durability 
of  the  settings,  fully  warrant  their  construction.  The 
results  obtained  in  many  large  plants  fully  sustain  this 
statement. 

The  exposed  portions  of  the  boiler  shells  above  the 
settings  are  covered  with  plastic  non-conducting  covering 
2$"  thick.  This  is  much  lighter  than  brick,  is  a  better 
non-conductor,  and  does  not  exert  a  sensible  thrust  upon 


BOILERS.  211 

the  setting  walls  as  a  brick  arch  does.  If  leaks  occur 
along  the  joints  of  the  covered  part  of  the  boiler,  they  are 
quickly  noted  by  the  discoloration  of  the  covering,  and 
may  be  stopped  before  the  injury  from  corrosion  occurs. 
The  illustrations  give  the  general  arrangement  of  the 
settings  above  described,  in  which  it  is  desired  to  combine 
durability  with  simplicity  in  design  and  construction,  and 
at  the  same  time  to  obtain  good  results  from  the  boilers, 
both  in  economy  and  in  capacity." 


CHAPTER    X. 

CHIMNEYS. 

85.  CHIMNEYS. —  Chimneys  are  to  carry  the  products 
of  combustion  away  from  the  boiler,  and,  by  so  doing, 
produce  a  draft  that  will  cause  fresh  air  to  enter 
the  furnace  and  carry  with  it  the  oxygen  to  be  used 


Fig.  98. 

in  combustion.  They  are  made  either  of  brick  or 
metal;  and  usually  have  either  an  octagonal  or  circular 
cross-section.  A  circular,  inside,  cross-section  is  better 
than  either  a  square  or  an  octagonal  cross-section,  as  it 
offers  less  resistance  to  the  flow  of  the  gases.  A  square, 
inside,  cross-section  is,  really,  equivalent  only  to  a  cir- 
cular cross-section  whose  diameter  is  equal  to  that  of  a 
(212) 


CHIMNEYS. 


213 


circle  inscribed  in  the  square ;  this  is  so  as  the  corners  of 
square  chimneys  become  almost  dead  spaces,  on  account 
of  the  excessive  resistance  there  to  the  flow  of  the  gases. 
The  passage  through  which  the  gases  pass,  after  leav- 
ing the  boiler  or  battery  of  boilers,  on  their  way  to  the 


chimney,  is  termed  the  "  breeching ;  "  it  may  be  large  or 
small,  long  or  short,  depending  upon  the  number  of  boil- 
ers connected  to  it  and  the  distance  from  the  boilers  to 
the  chimney. 

In  the  case  of  a  single  boiler,  or  a  small  battery  of  boil- 


214  STEAM    ENGINES    AND    BOILERS. 

ers,  the  chimney  is  usually  made  of  No.  16  sheet  iron, 
and  is  carried  directly  by  the  breeching.  Fig.  98  shows 
the  breeching  of  a  sheet  iron  stack  for  a  single  boiler  with 
a  half-arch  front  setting ;  and  Fig.  99  shows  the  breech- 
ing for  a  battery  of  two  boilers,  with  a  full-arch  front 
setting. 

In  the  case  of  a  large  battery  of  boilers,  a  number  of 
small,  sheet  iron  chimneys,  to  each  of  which  will  be  con- 
nected two  or  three  boilers,  may  be  used,  or  all  the 
boilers  may  be  connected  to  a  single  large  chimney. 

Brick  chimneys,  usually,  have  two  walls  with  an  air 
space  between  them.  The  inner  wall  may  extend  up  the 
whole  height  of  the  chimney  or  only  a  part  of  the  way  to 
the  top.  The  outer  wall  is  for  stability,  and  forms  the 
body  of  the  chimney;  while  the  inner  wall  is  simply  a 
lining  to  prevent  the  hot  gases  from  coming  in  contact 
with  the  outer  wall,  and  it  should  be  made  entirely  of  fire 
brick  laid  in  clay,  or,  at  least,  should  be  lined  with  fire 
brick.  This  lining  is  necessary,  as  ordinary  brick-work  will 
not  stand  the  heat  of  the  hot  gases  without  deteriorating 
very  much. 

Brick  chimneys  are  very  much  used,  although  they  are 
expensive,  and  are  apt  to  open  at  the  joints  and  let  cold 
air  leak  into  the  inside. 

In  Fig.  icois  shown  a  section  of  a  large  brick  chimney 

Iron  chimneys,  of  large  size,  made  of  thick  sheet  iron, 
are  becoming  more  and  more  extensively  used  every  day. 
They  are  usually  cheaper  than  brick  chimneys,  and  are 
perfectly  air  tight.  They  may  or  may  not  be  lined  with 
fire  brick,  although  it  is  preferable  to  have  them  lined. 

In  Fig.  101  is  shown  an  elevation  and  section  of  a  steel 
plate  chimney,  such  as  is  made  by  the  Philadelphia  En- 
gineering Works,  Philadelphia,  Pa. 

86.  DRAFT  OF  CHIMNEY. —  By  the  draft  of  a  chimney  is 
meant  the  difference  in  pressure  of  the  gases  in  the  chim- 


CHIMNEYS, 


215 


Fig.  100. 


Fig.  101. 


216  STEAM   ENGINES    AND    BOILERS. 

ney  and  that  of  the  air  on  the  outside,  measured  at,  or 
near,  the  base  of  the  chimney.  It  is  this  difference  in 
pressure,  or  draft,  that  makes  the  air  flow  into  the  furnace 
and  force  the  gases  out  through  the  top  of  the  chimney. 
When  the  draft  is  due  to  the  difference  in  temperatures 
of  the  gases  in  the  chimney  and  the  air  outside,  and  to 
the  height  of  the  chimney,  it  is  termed  a  natural  draft ; 
but  when  the  pressure  forcing  the  air  into  the  furnace  is 
that  due  to  a  fan  or  blower,  the  draft  is  termed  a  forced 
draft,  since  it  is  usually  much  greater  than  the  ordinary, 
natural,  draft.  Of  course,  there  is  no  sharp  line  of 
demarkation  between  natural  and  forced  drafts ;  as  a  nat- 
ural draft  may  be  very  high,  and  a  forced  draft  may  be 
very  low. 

The  draft  is  usually  spoken  of  as  being  of  so  many 
"  inches  of  water."  This  method  of  expressing  the  draft 
gives  the  head  of  water,  in  inches,  that  is  equivalent  to 
the  difference  between  the  pressure  of  the  air  and  that  of 
the  gases  inside  of  the  chimney.  The  number  of  inches 
of  draft  is  measured  by  means  of  a  U-tube,  shown  in  Fig. 
102.  The  legs  of  the  tube  are  first  filled  about  half  full 
with  water  ;  then,  one  end  of  the  tube  is  inserted  through 
a  hole  in  a  piece  of  cork  that  fits  tightly  into  an  opening 
in  either  the  breeching,  near  the  chimney,  or  the  base  of 
the  chimney  itself;  the  other  end  of  the  tube  is  left  open 
to  the  air.  The  water  will  stand  higher  in  the  leg  in 
communication  with  the  hot  gases  than  in  the  one  in 
communication  with  the  air;  and  the  distance,  in  inches, 
that  the  surface  of  the  water  in  the  one  leg  is  above  the 
surface  of  the  water  in  the  other  leg  is  the  draft  in  inches 
of  water. 

Except  in  the  case  of  very  high  chimneys,  the  draft  of 
furnaces  having  natural  draft  will  seldom  exceed  three- 
fourths  of  an  inch,  and  is  ordinarily  about  one-half  an 
inch.  The  draft  in  furnaces  using  forced  draft  is  only 
limited  by  the  ability  of  the  fan  or  blower  to  create  it. 


CHIMNEYS. 


217 


87.  VELOCITY  OF  THE  GASES  PASSING  THROUGH  THE 
CHIMNEY. —  The  velocity  of  the  flow  of  the  gases  through 
the  smallest  cross-section  of  the  chimney  is  determined 
by  the  law  of  the  flow  of  gases  under  a  small  pressure. 
We  know,  from  physics,  that  for  small  pressures,  the 
velocity,  in  feet  per  second,  with  which  a  gas  will  flow 


Fig.  102. 

from  a  vessel  in  which  the  unbalanced  pressure  per  square 
foot,  /,  is  that  equivalent  to  a  head,  h,  of  the  gas,  is 

(86)  v  =  y^h 

v  is  the  velocity  of  flow,  in  feet  per  second,  of  the  gas. 
g  is  equal  to  the  constant  32.  h  is  the  head,  in  feet  of 
gas,  equivalent  to  the  pressure,  p,  per  square  foot,  that 
causes  the  gas  to  flow. 

If  the  gas  has  a  density,  or  weight  per  cubic  foot,  of  Dt 


then 


=  p,  and  h  ==      . 


218  STEAM   ENGINES    AND    BOILERS. 

In  the  case  of  a  chimney,  the  pressure  causing  the  gas. 
to  flow  is  equal  to  the  difference  between  the  pressures 
inside  and  outside  of  the  chimney. 

Let  Fig.  103  represent  a  chimney,  whose  height  in  feet 
is  H,  with  an  opening  at  the  bottom.  Also,  let  PI  be  the 
pressure,  per  square  foot,  of  the  gases  inside  the  chim- 
ney ;  Po,  the  pressure,  per  square  foot,  of  the  air  outside 
the  chimney  ;  D\,  the  density  of  the  gases  inside  the 
chimney  ;  Do,  the  density  of  the  air  outside  ;  and  P,  the 
pressure,  per  square  foot,  of  the  air  at  the  top  of  the 
chimney. 

Then,  evidently,  P0  =  P  +  HDo  ;  Pl  =  P  +  HD^  ;  and 
the  pressure  that  forces  air  into  the  opening,  and  the 
gases  out  of  the  chimney,  is 

Po  —  Pi  =  H  (Do  -  A). 

The  head,  h,  in  feet  of  hot  gas  equivalent  to  the  pres- 
sure Po  —  Pi  is,  from  what  has  been  said  before,  equal  to 
the  pressure  divided  by  the  density  of  the  hot  gas. 
Therefore, 

Po-  A         „  (Do 
ks      _____      =H^- 

From  (86)  we  know  that  the  velocity  with  which  the 
hot  gas  will  tend  to  flow,  when  under  a  pressure  equiva- 
lent to  a  head  ht  is 


(88)  F=  12= 

Experience  has  shown,  however,  that  the  velocity  of 
the  gases  in  a  chimney  is  reduced  by  friction,  until  it  is 
only  from  one-third  to  one-half  what  it  would  be  if  there 
were  no  friction.  Therefore,  if  we  let  /£  represent  a  factor, 
varying  between  one-third  and  one-half,  by  which  the 
theoretical  expression  in  (88)  must  be  multiplied  in  order 
to  obtain  the  actual  value,  u,  of  the  velocity  of  the  flow 
of  the  gases,  we  have 


CHIMNEYS. 


219 


(89) 


The  density  of  air  at  32°  F.,  or  493°  absolute,  is  0.08, 
and  it  is  sufficiently  accurate  for  us  to  assume,  as  is  al- 
most true,  that  the  density  of  the  gases  in  the  chimney  is, 
also,  0.08  at  32°  F. 

Now,  if  the  absolute  temperature  of  the  air  outside  of 
the  chimney  is  To,  and  that  of  the  gases  inside  is  7i  we 


Fig.  103. 

know,  from  what  has  been   said  in    Chapter  I,  that,  since 
the  density  of  a  gas  is  inversely  as  its  volume, 


1 
— 

KO 


0.08  X  493 
--  _  -- 

TO 

0.08  X493 

"IT 


,  and 


220  STEAM   ENGINES    AND    BOILERS. 

Therefore, 

A  __  Ti_ 
A  =     To  ; 

and  the  expression  for  u,  as  given  in  (89),  becomes 
(90)  u  =  8 


The  temperature  of  the  gases  in  chimneys  is,  ordinarily, 
between  400°  F.  and  550°  F. ;  so  that  the  value  of  71  will 
be  between  861  and  ion.  The  temperature  of  the 
outside  air  varies  with  the  locality  and  the  seasons  of  the 
year,  but  it  may  be  assumed  as  60°  F.,  or  521°  absolute. 

7"1 

Therefore,  the  value  of  yr  may  be  taken  as  varying  from 

1.6  to  2. 

As  the  density  of  the  air  varies  greatly  from  time  to 
time,  depending  upon  the  amount  of  moisture  in  the  air, 
and  as  the  density  of  the  gases  inside  of  the  chimney  also 
varies  greatly,  the  value  of  u  can  never  be  very  accurately 
obtained  by  an  equation.  The  result  obtained  by  the 
use  of  (90)  is  apt  to  differ  more  or  less  from  the  true  value 
of  u,  because  in  (90)  it  has  been  assumed  that  the  temper- 
ature of  the  gases  is  the  same  at  all  parts  of  the  chimney, 
whereas  it  really  becomes  less  the  nearer  we  approach 
the  top. 


APPENDIX. 

CARE    OF    BOILERS. 

As  it  is  very  important  that  everbody  having  anything 
to  do  with  the  operation  of  a  boiler  plant  should  know 
how  to  care  for  the  boilers,  there  is  inserted,  here,  the 
rules  to  be  observed  in  order  to  prevent  accidents,  to 
economize  fuel,  and  to  preserve  the  boiler,  that  are  given 
by  the  Fidelity  and  Casualty  Company  in  its  little  book, 
The  Engineer's  Manual. 

How  to  Prevent  Accidents. 

1.  SAFETY    VALVES. —  These      should    be    of     ample 
size  and   kept   in  working  order.     The  valve  should  be 
tried  daily  ;  this  is  best  done  by  allowing  the  pressure  to 
rise  gradually  until  the  valve  just  "simmers,"  noting  the 
pressure  by  the  steam  gauge  at  the  moment.     Freedom 
of  action   may  of  course  be   ascertained  by  hand,  but  it 
cannot  be  known  by  this  means  that  the  valve  will  blow 
off  when  the  proper  pressure    is  attained.     Neglect  and 
overloading  of  this  most   important  adjunct  are    prolific 
causes  of  boiler  explosions.     Each  boiler  should  have  its 
own  safety  valve,  and  no  stop  valve  should  be  permitted 
between  it  and  the  boiler.     See  cut  "  A  "  (not  given  here). 
This  illustrates  the  worst  combination  of  safety  and  stop 
valves  that  could  well  be  contrived. 

2.  PRESSURE  GAUGE. —  It  is   absolutely  necessary  that 
the  pressure  gauge  should  be  trustworthy,  and  if  there  is 
any  reason  to  question  its  readings,  it  should  be  compared 
with  one  known  to  be  accurate.     The  gauge  should  be 

(221) 


222  STEAM   ENGINES    AND    BOILERS. 

fitted  to  a  "  loop  "  filled  with  water,  which  transmits  the 
pressure  and  prevents  contact  of  steam  with  the  gauge 
spring.  Attach  the  gauge  directly  to  the  boiler  and  not 
to  the  steam  pipe,  to  prevent  fluctuations  of  pressure 
readings. 

3.  WATER  LEVEL.  —  Before  starting,    make  sure    that 
there  is  plenty  of  water  in  the  boiler  by  trying  the  gauge 
cocks.     While  running  do  not  depend  on  the  gauge  glass, 
but  try  the  gauge  cocks  often.     The  water  line  should  be 
kept  at  a  regular  height,  and  should  never  be  less  than 
three  or  four  inches  above  the  "  fire  line."     The  gauge 
glass  should  be  blown  out  frequently  to  see  that  it  is  not 
chojced ;  it  is  an   excellent  plan  to  try  the  gauge  cocks 
every  fifteen   minutes.     Both  gauge   and  cocks  must  be 
kept  clean. 

4.  DAMPER. —  Do  not  close  the  damper  entirely  while 
there  is  fire  on  the  grates,  as  gas  may  collect  in  the  tubes 
and  cause  an  explosion. 

5.  FEED  PUMP  OR  INJECTOR. —  These  should  be  kept  in 
order,  and  should  be  of  ample  size  for  all  requirements. 
The  feed  pump,  however,  ought  not  to  be  so  large  as  to 
render  it  difficult  to  feed  the  boiler  continuously  at  a  slow 
rate  of  speed.     It  is  always  safer  to  have  two  means  of 
feeding.     An  injector  should  be  used  when  no  feed-water 
heater  is  provided,  as  it  prevents  the  contraction  of  tubes 
and  plates  where  the  feed  water  comes  in  contact  with 
them. 

6.  Low  WATER. —  The  blow-out   apparatus  should  be 
kept  tight,  as   any  leakage  here   may  give   rise  to    low 
water,  with  the  result  of  overheating  the  plates.     In  case 
of  low  water,  fresh  coal,  or  better  still,  wetted  ashes,  must 
be  thrown  on  the  fire  at  once.     Do  not  turn  on  the  feed, 


APPENDIX.  223 

though  if  already  in  motion,  allow  it  to  continue,  nor  start 
or  stop  the  engine,  or  lift  the  safety-valve  until  the  boiler 
has  cooled  down.  After  a  case  of  low  water  the  tube 
ends  in  the  upper  rows  should  be  examined  for  leaks. 

7.  INCRUSTATION,  CORROSION. —  Boilers  should  be  kept 
free  from  scale,  as  its  presence  increases  the  liability   of 
burning   or    cracking   the    plates    and    predisposes     to 
explosion.     The  surest  method  for  preventing   internal 
corrosion  is  to  abandon  the  use  of  the  water  which  causes 
it,  but  if  this  is  impracticable,  a  sharp  lookout  should  be 
kept  for  defects.     Leaks  of  seams  and  fittings,    drippings 
from  pipes,  exposure  to  the  weather,  contact  of  the  boiler 
with  brick-work,  etc.,  are  causes  of  external  corrosion, 
and  should  be  at  once  remedied. 

8.  BLISTERS,    CRACKS,    AND     BURNT   PLATES. —  When 
these  occur  they  should  receive  attention  at  once.    Burnt 
places  and  blisters  should  be  cut  out  and  a  patch  put  on 
inside   the   boiler   to   avoid    making   a    pocket   for    the 
collection  of  sediment. 

9.  FUSIBLE    PLUGS. —  These  are    required   by   law   in 
some  States.     To  keep   them  in   an    efficient  condition 
their  surfaces,  both  on  the  fire  and  water  sides,  must  be 
often  scraped  clean,  but  notwithstanding   all  precautions, 
they  are  unreliable. 

10.  STARTING  THE  ENGINE. —  The    engine  should   be 
started  slowly,  in  order  not  to  make  a  violent  change  in 
the    condition    of    the   water   and      steam,   and     when 
possible,  the  engine  should  be  stopped  gradually.     The 
sudden  opening  or  closing  of  a  large  stop-valve  may  pro- 
duce a  violent  rush  of  steam  and  water  against  that  part 
of  the  boiler  whence  the  steam  is   drawn,  the  percussion 
of  which  may  be  sufficient  to  rupture  the  boiler. 


224  STEAM   ENGINES    AND    BOILERS. 

How  to  Save  Fuel. 

1.  FIRING. —  The  fire  should  be  kept  level  and  of  some- 
what greater  thickness  at  the  bridge  wall.     This  promotes 
a  uniform  consumption  of  fuel,  as  the  air  passes  more 
freely  through  the  fire  near  the  bridge  and  the  greater 
thickness  retards  its  passage.     Fuel  supplied  regularly  in 
small    quantities,    combined  with   an    even    distribution, 
produces  the  best  results.     When  anthracite  coal  is  used, 
the  average  thickness  of  the  fire  should  be  6  to  8  inches  ; 
with    bituminous  coal,  it  should  be  8  to  10  inches;  with 
coke,  10   to  12  inches.     If  the  draft  is  poor,  however,  a 
thin  fire  must  be  used.     Do  not  fire  with  large  lumps.     No 
fragment  ought  to  be  larger  than  a  man's  fist. 

Complete  combustion  is  only  attained  when  the  fuel  is 
burning  with  a  bright  flame  all  over  the  grate.  Blue 
flames,  dark  spots  and  smoke  are  evidences  of  the  lack 
of  the  necessary  air  which  ought  to  be  supplied  above 
the  grate.  Fires  should  be  "  cleaned  "  no  oftener  than 
necessary.  In  using  a  caking  coal,  it  is  advantageous  to 
make  use  of  a  "  coking  fire,"  i.  e.,  firing  in  front  and 
breaking  up  with  a  slice  bar,  and  shoving  back  when 
coked.  The  practice  of  wetting  coal  before  throwing  it 
on  the  fire  is  a  bad  one,  as  it  wastes  heat  and  produces 
corrosion. 

2.  FEED- WATER. —  Heating  the  feed-water,  either  by 
means  of  exhaust  steam  or  the  waste  gases  in  the  chim- 
ney, adds  to  the  economy  of  a  steam  plant.     Each  in- 
crease in  the   temperature  of  the    feed-water   of  1 1°  F. 
means  a  saving  of  fuel  of  one  per  cent.     No  saving  in 
fuel  is  effected  by  the  use  of  an  injector,  but  the  employ- 
ment of  one  promotes  the  longevity  of  a  boiler  by  intro- 
ducing the  feed-water  at  a  temperature  so  high  that  no 
injurious    contractions  are   caused   in   any   part    of   the 
boiler. 


APPENDIX.  225 

3.  CLEANING. —  The  heating  surfaces  of  a  boiler,  both 
inside  and  out,  should  be  kept  clean,  in  order  to  prevent 
a  serious  waste  of  fuel.     The  thickness   of  the  soot  or 
scale   which  is  allowed   to   accumulate    ought   never  to 
exceed  T^  of  an  inch. 

4.  LEAKS   IN   BRICK-WORK. —  Cracks   or   openings    m 
the  brick-work  should  be  carefully  stopped.     The  admis- 
sion of  air,  except  at  the  places  provided  for  it,  impairs 
the  draft,  cools  the    gases  on  their  way  to  the    tubes, 
and  sometimes  causes  jets  of  flame  to  impinge  so  strongly 
on  the  shell  as  to  injure  the  plates. 

5.  COVERING. —  Radiation  from  the  dome  and  the  top 
of  the  boiler  is  a  source  of  waste.     A  covering  of  asbestos 
or  other  suitable  non-conducting  material  should  be  pro- 
vided as  a  protection. 

6.  BLOWING  OUT. —  The  bottom  blow-out  cock  should 
be  kept  tight  to  prevent  loss  by  leakage.     A  plug  cock  is 
the  simplest,  surest  and  most  durable  valve  for  this  pur- 
pose.    When  the  feed  water  is  of  a  hard  or  muddy  nature, 
the   boiler  should  be  blown    out    frequently.     A    boiler 
should  be  emptied  every  week  or  two,  and  filled  afresh. 
The  proper  manner  to  use  a  surface  blow-off  is  to  open  it 
for  about  fifteen  seconds    every  hour   rather  than  for  a 
longer  time  at  greater  intervals. 

How  to  Lengthen  the  Life  of  the  Boiler. 

1.  BANKING  FIRES. —  Contraction  and  expansion,  caused 
by  change  of  temperature,  shorten  the  life  of   a  boiler. 
For   this  reason  it   is  better  to   bank  the  fires  at  night 
instead  of  drawing  them. 

2.  LEAKS, —  Leaks,  whether  in  boiler  or  fittings,  should 
be  repaired  at  once.     Leaks  often  give  rise  to  corrosion. 

15 


226  STEAM   ENGINES    AND    BOILERS. 

3.  FILLING  UP.  —  Wear  and  tear  of  a  boiler,    arising 
from  unequal  expansion  and  contraction,  is  increased  by 
allowing  the  feed- water  to  enter  at  too  low  a  temperature. 
If  the  use  of  cold  water  is  unavoidable,  the    feed-pipe 
should  always  be  extended  into  the  interior  of  the  boiler. 
It  should  enter  horizontally  through  the  front  head,  near 
one  side,  and   a  few  inches  below  the  water-line,  thence 
extending  back  to  within  a  few  feet  of  the  back  head, 
crossing  over    and  discharging   downward    between    the 
tubes  and  shell.     By  this  means  the  feed-water  is  heated 
nearly  to  the  temperature  of  water  in  the  boiler,  and  is 
discharged  at  the  coolest  part  of  the  boiler.     The  use  of 
an  injector  or  feed-water  heater  renders  this  extension  of 
the  feed-pipe  unnecessary. 

4.  BLOWING  OUT. —  A  boiler  should  never  be  emptied 
while  the  brick-work  is  hot.     When  this  is  done  the  sedi- 
ment is  baked  on  the  plates,  making  it  difficult  to  remove. 

5.  RAPID  FIRING. —  Steam  should  be  raised  slowly  in 
a  boiler  having  thick  plates  or  seams  exposed  to  the  fire, 
else  overheating  or  burning  results.     The  greatest  effect 
of  a  fire  on  a  boiler   bottom  takes   place  immediately 
behind  the  bridge,  and  if  a  seam  is  located  here  there  is 
liability  of  burning  the  lap.     It  is  best  in  such  cases  to 
change  the  position  of  the  bridge,  so  that  the  seam  comes 
over  the  bridge,  or  better  still,  over  the  furnace. 

6.  MOISTURE. —  The  exterior  of  a   boiler    should  be 
protected  from  moisture,  as  it  brings  about  corrosion  and 
consequent  weakening  of  the  boiler. 

7.  GALVANIC     ACTION. —  Sometimes    boilers    may   be 
protected  from  the  action  of  corrosive  agents  present  in 
the  water  by  means  of  zinc.     As  a  rule  one  square   inch 
of  surface  of  zinc  to    every  fifty  pounds  in  the  boiler  is 


APPENDIX.  227 

sufficient.  The  plates  should  be  placed  in  perfect  metallic 
contact  with  the  iron  and  renewed  as  they  are  wasted  by 
oxidation. 

8.  DISUSE  OF  BOILER. —  If  it  is  intended  not  to  use  the 
boiler  for  some  time,  the  boiler  should  be  emptied  of  its 
water,  dried  thoroughly  by  pans  of  charcoal,  and  after 
placing  pans  of  lime  in  the  interior,  closed  to  prevent 
oxidation.  If  this  is  impracticable,  the  boiler  should  be 
filled  with  water  in  which  common  soda  is  dissolved. 


TABLE     I . 


PROPERTIES    OF    STEAM. 


Pressure 
by  the 
Gauge. 

Temperature. 

Total 
Heat  above 
32°. 

Latent 
Heat. 

Vol.  of 
one  Ib.  of 
Steam. 

—13 

119. 

1118. 

1031. 

223. 

—12 

137. 

1124. 

1019. 

135. 

—11 

150. 

1128. 

1010. 

98.9 

—10 

160. 

1131. 

1003. 

78.3 

—  9 

168. 

1133. 

997. 

65.0 

—  8 

175. 

1135. 

992. 

55.9 

—  7 

181. 

1137. 

988. 

48  9 

—  -  6 

187. 

1139. 

984. 

43.6 

—  5 

191.8 

1140.4 

980.1 

39.31 

-.-  4 

197. 

1142. 

977. 

35  8 

—  3 

201. 

1143. 

974. 

33.3 

—  2 

205. 

1144. 

971. 

30.6 

-..  1 

208. 

1146. 

968. 

28.4 

0 

212.0 

1146.6 

965.7 

26.56 

1 

215. 

1148. 

964. 

25.0 

2 

219. 

1149. 

961. 

23.6 

3 

222. 

1150. 

959. 

22.3 

4 

224. 

1150. 

957. 

21.2 

5 

227.1 

1151.2 

955.1 

20.16 

6 

230. 

1152. 

953. 

19.3 

7 

232. 

1153. 

952. 

18.4 

8 

235. 

1154. 

950. 

17.7 

9 

237. 

1154. 

948. 

17.0 

10 

239.4 

1154.9 

946.4 

16.30 

11 

242. 

1156. 

944. 

15.7 

12 

244. 

1156. 

944. 

15.2 

13 

246. 

1157. 

942. 

14.6 

14 

248. 

1158. 

941. 

14.2 

15 

249.7 

1158.1 

939.3 

13.71 

230 


STEAM   ENGINES    AND    BOILERS. 


Pressure 
by  the 
Gauge. 

Temperature. 

Total 
Heat  above 
32°. 

Latent 
Heat. 

Vol.  of 
one  Ib.  of 
Steam. 

16 

252. 

1159. 

938. 

13.3 

17 

253. 

1159. 

937. 

12.9 

18 

255. 

1160. 

935. 

12.5 

19 

^257. 

1160. 

934. 

12.2 

20 

258.7 

1160.9 

932.7 

11.85 

21 

260. 

1161. 

932. 

11.6 

22 

262. 

1162. 

931. 

11.3 

23 

264. 

1162. 

929. 

11.0 

24 

265. 

1163. 

928. 

10.7 

25 

266.7 

1163.3 

927.1 

10.36 

26 

268. 

1164. 

926. 

10.2 

27 

270. 

1164. 

925. 

9.95 

28 

271. 

1165. 

924. 

9.75 

29 

273. 

1165. 

923. 

9.54 

30 

273.9 

1165.5 

922.0 

9.34 

31 

275. 

1166. 

921. 

9.16 

32 

277. 

1166. 

920. 

8.98 

33 

278. 

1167. 

919. 

8.81 

34 

279. 

1167. 

918. 

8.63 

35 

280.5 

1167.5 

917.3 

8.45 

36 

282. 

1168. 

917. 

8.31 

37 

283. 

1168. 

916. 

8.16 

38 

284. 

1169. 

915. 

8.02 

39 

285. 

1169. 

914. 

7.87 

40 

286.5 

1169.3 

913.0 

7.73 

41 

288. 

1170. 

912. 

7.61 

42 

289. 

1170. 

911. 

7.48 

43 

290. 

1170. 

911 

7.36 

44 

291. 

1171. 

911. 

7.23 

45 

292.2 

1171.1 

909.0 

7.11 

46 

293. 

1171. 

908. 

7.01 

47 

294. 

1172. 

907. 

6.91 

48 

295. 

1172. 

907. 

6.81 

49 

296. 

1172. 

906. 

6.71 

50 

297.5 

•  1172.7 

905.2 

6.61 

51 

299. 

1173. 

904. 

6.52 

52 

300. 

1173. 

904. 

6.43 

APPENDIX, 


231 


Pressure 
by  the 
Gauge. 

Temperature. 

Total 
Heat  above 
32°. 

Latent 
Heat. 

Vol.  of 
one  Ib.  of 
Steam. 

53 

301. 

1174. 

903. 

6.34 

54 

302. 

1174. 

902. 

6.25 

55 

302.4 

1174.2 

901.6 

6.16 

56 

303. 

1174. 

901. 

6.08 

57 

304. 

1175. 

900. 

6.00 

58 

305. 

1175. 

900. 

5.93 

59 

306. 

1175. 

899. 

5.85 

60 

307.1 

1175.6 

898.4 

5.77 

61 

308. 

1176. 

898. 

5.70 

62 

309. 

1176. 

897. 

5.63 

63 

310. 

1176. 

897. 

5.57 

64 

311. 

1177. 

896. 

5.50 

65 

311.5 

1176.9 

895.1 

5.43 

66 

312. 

1177. 

895. 

5.37 

67 

313. 

1178. 

894. 

5.31 

68 

314. 

1178. 

893. 

5.25 

69 

315. 

•     1178. 

893. 

5.19 

70 

315.8 

1178.2 

892.1 

5.13 

71 

317. 

1179. 

892. 

5.08 

72 

317. 

1179. 

891. 

5.02 

73 

318. 

1179. 

890. 

4.97 

74 

319. 

1179. 

890. 

4.91 

75 

319.8 

1179.4 

889.1 

4.86 

76 

321. 

1180. 

889. 

4.81 

77 

321. 

1180. 

888. 

4.77 

78 

322. 

1180. 

887. 

4.72 

79 

323. 

1180. 

887. 

4.68 

80 

323.7 

1180.6 

886.3 

463 

81 

324. 

1181. 

886. 

4.59 

82 

325. 

1181. 

885. 

4.54 

83 

326. 

1181. 

885. 

4.50 

84 

327. 

1182. 

884. 

4.45 

85 

327.4 

1181.7 

883.6 

4.41 

86 

328. 

1182. 

883. 

4.37 

87 

329. 

1182. 

883. 

4.33 

88 

330. 

1182. 

882. 

4.28 

89 

330. 

1183. 

881. 

4.24 

232 


STEAM    ENGINES    AND    BOILERS. 


Pressure 
by  the 
Gauge. 

Temperature. 

Total 
Heat  above 
32°. 

Latent 
Heat. 

Vol.  of 
one  Ib.  of 
Steam. 

90 

330.9 

1182.8 

881.0 

4.20 

91 

332. 

1183. 

881. 

4.16 

92 

332. 

1183. 

880. 

4.13 

93 

333. 

1184. 

880. 

4.09 

94 

334. 

1184. 

879. 

4.06 

95 

334.4 

1183.9 

878.5 

4.02 

96 

335. 

1184. 

878. 

4.00 

97 

336. 

1184. 

878. 

3.97 

98 

336. 

1185. 

877. 

3.93 

99 

337. 

1185. 

877. 

3.90 

100 

337.6 

1184.9 

876.0 

3.86 

101 

338. 

1185. 

876. 

3.83 

102 

339. 

1185. 

875. 

3.80 

103 

340. 

1186. 

875. 

3.77 

104 

340. 

1186. 

874. 

3.74 

105 

340.9 

1185.9 

873.8 

3.71 

106 

342. 

1186. 

873. 

3.68 

107 

342. 

1186. 

873. 

3.65 

108 

343. 

1186. 

872. 

3.63 

109 

343. 

1187. 

872. 

3.60 

110 

343.9 

1186.8 

871.4 

3.57 

111 

345. 

1187. 

871. 

3.55 

112 

345. 

1187. 

871. 

3.52 

'  113 

346. 

1187. 

870. 

3.50 

114 

346. 

1188. 

870. 

3.47 

115 

346.9 

1187.7 

869.3 

3.45 

116 

348. 

1188. 

869. 

3.43 

117 

348. 

1188. 

868. 

3.40 

118 

349. 

1188. 

868. 

3.38 

119 

349. 

1189. 

868. 

3.35 

120 

349.8 

1188.6 

867.1 

3.33 

121 

350. 

1189. 

867. 

3.31 

122 

351. 

1189. 

866. 

3.28 

123 

352. 

1189. 

866. 

3.26 

124 

352. 

1189. 

865. 

3.23 

125 

352.6 

1189.5 

864.9 

3.21 

126 

353. 

1190. 

865. 

3.19 

127 

354. 

1190. 

864. 

3.17 

APRENDIX. 


233 


Pressure 
by  the 
Gauge. 

Temperature. 

Total 
Heat  above 
32°. 

Latent 
Heat. 

Vol.  of 
one  Ib.  of 
Steam. 

128 

354. 

1190. 

864. 

3.14 

129 

355. 

1190. 

863. 

3.12 

130 

355.4 

1190.3 

863.0 

3.10 

131 

356. 

1191. 

863. 

3.08 

132 

357. 

1191. 

862. 

3.06 

133 

357. 

1191. 

862. 

3.05 

134 

358. 

1191. 

861. 

3.03 

135 

358.0 

1191.1 

861.0 

3.01 

136 

359. 

1191. 

861. 

2.99 

137 

359. 

1192. 

860. 

2.97 

138 

360. 

1192. 

860. 

2.96 

139 

360. 

1192. 

860. 

2.94 

140 

360.7 

1191.9 

859.1 

2.92 

141 

361. 

1192. 

859. 

2.90 

142 

362. 

1192. 

858. 

2.88 

143 

362. 

1192. 

858. 

2.87 

144 

363. 

1193. 

858. 

2.85 

145 

363.2 

1192.7 

857.2 

2.83 

146 

364. 

1193. 

857. 

2.81 

147 

364. 

1193. 

857. 

2.80 

148 

365. 

1193. 

856. 

2.78 

149 

365. 

1193. 

856. 

2.77 

150 

365.7 

1193.4 

855.4 

2.75 

NOTE.— Although  the  quantities  in  the  table  are  not  carried  out  to  as  many 
significant  figures  as  in  many  tables,  they  are  sufficiently  exact  for  practical 
purposes.  The  volumes  have  been  calculated  upon  the  assumption  that  the 
mechanical  equivalent  is  778,  instead  of  772.  All  the  volumes  have  been  calcu- 
lated up  to  201bs.  pressure;  above  that  they  have  been  calculated  only  every 
five  pounds,  and  the  intermediate  values  interpolated. 


234 


STEAM    ENGINES    AND    BOILERS, 


TABLE    II. 


HYPERBOLIC    LOGARITHMS. 


Number. 

Hyperbolic 
Logarithm. 

Number. 

Hyperbolic 
Logarithm. 

Number. 

i 

Hyperbolic 
Logarithm. 

Number. 

Hyperbolic 
Logarithm. 

1.0 

0.00 

3.5 

.25 

6.0 

1.79 

8.5 

2.14 

1.1 

0.10 

3.6 

.28 

6.1 

1.81 

8.6 

2.15 

1.2 

0.18 

3.7 

.31 

6.2 

1.82 

8.7 

2.16 

1.3 

0.26 

3.8 

.34 

6.3 

1.84 

8.8 

2.17 

1.4 

0.34 

3.9 

.36 

6.4 

1.86 

8.9 

2.19 

1.5 

0.41 

6.5 

1.87 

1.6 

0.47 

4.0 

.39 

6.6 

1.89 

9.0 

2.20 

1.7 

0.53 

4.1 

.41 

6.7 

1.90 

9.1 

2.21 

1.8 

0.59 

4.2 

.44 

6.8 

1.92 

9.2 

2.22 

1.9 

0.64 

4.3 

1.46 

6.9 

1.93 

9.3 

2.23 

4.4 

1.48 

9.4 

2.24 

2.0 

0.69 

4.5 

1.50 

7.0 

1.95 

9.5 

2.25 

2.1 

0  74 

4.6 

1.53 

7.1 

1.96 

9.6 

2.26 

2.2 

0.79 

4.7 

1.55 

7.2 

1.97 

9.7 

2.27 

2.3 

0.83 

4.8 

1.57 

7.3 

1.99 

9.8 

2.28 

2.4 
2.5 

0.88 
0.92 

4.9 

1.59 

7.4 
7.5 

2.00 
2.01 

9.9 

2.29 

2.6 

0.96 

5.0 

1.61 

7.6 

2.03 

10.0 

2.30 

2.7 

0.99 

5.1 

.63 

7.7 

2.04 

10.1 

2.31 

2.8 

1.03 

5.2 

.65 

7.8 

2.05 

10.2 

2.32 

2.9 

1.06 

5.3 

.67 

7.9 

2.07 

10.3 

2.33 

5.4 

.69 

10.4 

2.34 

3.0 

1.10 

5  5 

.70 

8.0 

2.08 

10.5 

2.35 

3.1 

1.13 

5.6 

.72 

8.1 

2.09 

10.6 

2.36 

3.2 

1.16 

5.7 

.74 

8.2 

2.10 

10.7 

2.37 

3.3 

1.19 

5.8 

1.76 

*  8.3 

2.12 

10.8 

2.38 

3.4 

1.22 

5.9 

1.78 

8.4 

2.13 

10.9 

2.39 

APPENDIX. 


235 


o 

ri  I 

i-  5 

iJ 

H    » 


8 


§ 


jo  earn 


f^  —•  o  ^s  oc  i> 


<M  —  O  CJ  L^  <£>  »O  -rf  CO  TM  I-H   O  Ci  QO  l^-  <X>  >O  ^ 


'-^OGOt^ 


'O^ 


OOOOOOOOOOOOOOOOO<N 

i-HT-(^HT-lrHr-'i-li-Hr-(THCM(M 


236 


STEAM   ENGINES   AND   BOILERS. 


TABLE  IV. 

HEATING  POWER  OF  FUELS. 


COMBUSTIBLE. 

C 

H 

0 

N 

Q 

Ash. 

%%*i 

D     -    0>    3 
^A& 

Wood,  air  dried  
Peat  

40.4 
40.8 
46.1 

86.5 

84.9 

85.3 
50.1 
643 
83.78 
82.12 
77.90 
78.53 

69.80 

83.74 
82.70 

72  29 

79.81 
91.50 

81.32 

4.90 
3.30 
4.60 

12.00 

13.70 

13.90 
3.90 
4.20 
4.79 
5.31 
5.32 
5.61 

5.26 

4.52 

4.77 

6.53 

5.98 
3.50 

32.70 
26.30 
23.60 

1.50 

1.40 

0.80 
13.70 
10.00 
4.15 
5.69 
9.53 
9.69 

8.35 

0.54 

8.81 

8.28 

4.80 
2.60 

0.90 
1.00 
1.00 



1.20 
7.70 
1.50 

6400 
6800 
7600 

19800 

19200 

18100 
10300 
11000 
15100 
15200 
14600 
14900 

12600 

14400 
14000 

13400 

14400 
15200 

12200 

"    air  dried  
Petroleum,   crude, 
from  Baker,  Russia 
Petroleum,      heavy 
crude,  from  Penn- 
sylvania   
Petroleum,    common, 
from  Virginia  
Lignite,  American  
*'        Australian... 
Coal   Welsh  

0.90 
1.00 
0  98 
1.35 
1.30 
1.00 

1.33 

1.50 
1.74 

1.50 
1.50 

1.50 
0.60 
1.43 
1.24 
1.44 
1.11 

2.02 

1.60 
0.98 

0.43 
1.35 

0.67 

13.20 
10.00 
4.91 
3.77 

4.88 
4.03 

6.90 

6.63 
1.00 

2.72 

6.48 

10.96 

*'     Newcastle  

"     Lancashire  
«'     Scotch  

"     Big    Muddy, 
"     Jackson  Co.,  Ill 
"     Johnson      Co., 
Arkansas  
11     Block   Id  

"     Hocking  Valley, 
Ohio  

"     Coking,     Pitts- 
burgh, Pa  
"     Anthracite  
"      Penn- 
sylvania, Buck- 
wheat   

C  means  per  cent  of  carbon  contained  in  the  combustible  ; 
H,  the  per  cent  of  hydrogen  ;  O,  the  per  cent  of  oxygen;  N, 
the  per  cent  of  nitrogen,  and  S,  the  per  cent  of  sulphur. 


PROB  LEMS. 

1.  How  much  work  is  done  in  lifting  a  weight  of  20  Ibs. 
through  a  height  of  20  ft.  ?  Ans.,  400  ft. -Ibs 

2.  How   much   work  is   done   in   moving   a   weight   of 
100  Ibs.  along  a  horizontal  plane  surface  against  a  resist- 
ance  of   10  Ibs.   through  a  distance  of  6  ft.? 

Ans.,  60ft.-lbs. 

3.  If  the  resistance   to  be   overcome   on   a  railroad  is 
10  Ibs.  for  each  ton  of  weight  of  the  cars,  what  horse- 
power will  be  required  to  move  a  train  of  cars  weighing 
100  tons  at  a  speed  of  40  miles  per  hour? 

Ans.,  107  horse-power. 

4.  How  many  units  of  heat  per  minute  are  equivalent 
to  one  horse-power?  Ans.,  42.4. 

5.  A  piece  of  iron  weighing  5  Ibs.  is  heated  to  212  de- 
grees and  then  dropped  into  a  vessel  containing  16.5  Ibs. 
of  water  at  60  degrees.     If  the  temperature  of  the  water 
is  increased  5  degrees  by  the  heat  from  the  iron,  what  is 
the  specific  heat  of  the  iron?  Ans.,  0.112. 

6.  The  specific  heat,  cp,  of  air  at  constant  pressure,  ex- 
pressed in  heat  units,  is  0.24.     What  is  the  specific  heat 
expressed  in  ft. -Ibs.  at  constant  pressure,  Kp,  and  at  con- 
stant volume,  Kyl 

Ans.,  Kp=  186.7  ft.-lbs.,  K,=  134.4  ft.-lbs. 

7.  A  quantity  of  air  at   a  temperature   of  60  degrees 
under  a  pressure  of  14.7  Ibs.  per  square  inch,  has  a  volume 
of   5   cubic  feet.     What  is  the   volume   of  the   same   air 

(237) 


238  STEAM    ENGINES    AND    BOILERS. 

when  its  temperature  is  changed  to  120  degrees  at  con- 
stant   pressure?  Ans.,  5.57  cub.  ft. 

8.  The  volume  of  a  quantity  of  air  at  a  temperature  of 
60  degrees  under  a  pressure  of  14.7  Ibs.  per  square  inch 
is  10  cub.  ft.     What  is  the  volume  of  the  same  air  when 
the  pressure  is  changed  at  constant  temperature  to  60 
Ibs.   per  square  inch?  Ans.,  2.45  cub.  ft. 

9.  Assume  that  the  initial  pressure,  volume,  and  abso- 
lute temperature  of  a  gas  are  Plf  Vly  and  7\;    and  that 
after  a  change  the  final  pressure,  volume,  and  absolute 
temperature  are  P2,  V2  and  T2.     Prove  that 


Let  the  pressure  remain  constant  at  Pl  while  the  tem- 
perature is  changed  from  7\  to  T2.  The  volume  will 
change  from  Vt  to  some  volume  that  we  may  call  V . 
From  (7)  we  have 

Vl     V 

(a)  -Y=~r 

1  1         1  2 

Now  let  the  absolute  temperature  remain  constant  at 
T2  while  the  pressure  is  changed  from  Pl  to  P2.  The 
volume  will  change  during  this  change  of  pressure  from 
V  to  V2.  From  (8)  we  have 

(b)  P,  V>  =  P2  V2. 
Multiply  (a)  by  (b)  and  we  have 

P,  Vl  V       P2  V2  V 


10.  The  volume  of  a  quantity  of  air  at  70  degrees 
under  a  pressure  of  16  Ibs.  per  square  inch  is  20  cubic 
feet.  What  is  the  temperature  of  this  air  when  the  vol- 
ume is  4  cubic  feet  and  the  pressure  is  70  Ibs.  per  square 
inch?  '  Ans.,  T=  464.6,  and  *  =  3.6. 


PROBLEMS.  239 

11.  What  is  the  weight  of  the  quantity  of  air  which 
occupies  a  volume  of  10  cubic  feet  at  a  temperature  of 
100  degrees  under  a  pressure  of  50  Ibs.  per  square  inch? 

When  the  pressure  is  in  pounds  per  square  foot,  we  know 

P  V 
that—jr-  —  w  53.15,  where  w  is  the  weight  of  the  air  in 

__  PV  50X144X10 

pounds.  .  53357-  (461  +  100)  53.15=  2'4 

12.  How  much  work  is  done  by  a  quantity  of  air  while 
expanding  under  a  constant  pressure  of  80  Ibs.  per  square 
inch  from  a  volume  of  2  cubic  feet  to  a  volume  of  6  cubic 
feet? 

For  expansion  at  constant  pressure,  the  work  is  equal 
to  the  pressure  per  square  foot  multiplied  by  the  change 
of  volume,  or 


P  =  80X144,  F2  =  6, 
Work  =  80X144  (6  -2)  =  46080  ft.-lbs. 

13.    How  much  heat,  expressed  in  foot-pounds,  must  be 
given  to  the  air  during  the  expansion  in  Problem  12? 


We  know  that  H  =  S  +  L  +  W.  For  a  perfect  gas  whose 
weight  is  w  we  know  that  S  =  wKv(T2  —  7\),andL  =  O. 
In  this  case  W  =  Pl(V2-V1).  Therefore, 

H=WKV  (Tt-Tj+Pt  (v—vj. 

But 
Pl  V2  =  R  w  T2  and  P,  V,  =  R  w  7\.    Hence  w  T2  =  ?^l  and 

p  y 
w  7\  =  —  —  L.    Put  for  w  T2  and  w  7\  their  values  and  get 


240  STEAM    ENGINES    AND    BOILERS. 


Hence, 

H=P1(F3-.yi)^j  =  80Xl44(6-.2)|g 

=  158,500  ft.-lbs. 

14.    How  much  heat  is  given  to  a  quantity  of  air  while 

P      P 
it  changes  in  such  a  manner  that  7-=-^,  from   an   initial 

volume  of  9.23  cubic  feet  under  a  pressure  of  100  Ibs. 
per  square  inch,  to  a  volume  of  18.46  cubic  feet  under  a 
pressure  of  200  Ibs.  per  square  inch? 

* 


As  before,  H  =  S  +  W;  and 
S  =  w  Kv  (T2  —  rj;  where 
w  is  the  weight  of  the  air; 
T2  the  final  absolute  tem- 
perature; and  Tj  the  initial 
absolute  temperature. 


W=area  abed,  in  the  figure, 


* 
£4 

P    V 
-2,  and  T,=  ^-^.    Therefore, 


w 


_P2V2-P1V1 
H= 


200  X  144  X  18.46  -  100  X  144  X  9.23 
1.41  -  1 

300X144(18.46-9.23) 
2 

1,172,000  ft.-lbs. 


PROBLEMS.  241 

15.  What  fraction  of  the  heat  in  Problem  14  is  trans- 
formed into  work?  Ans.,  0,17. 

16.  How  much  heat  must  be  given  to  a  quantity  of  air 
which  expands  isothermally,  at  a  temperature  of  60  de- 
grees, from  a  valume  of  0.83  cubic  feet  under  a  pressure 
of  60  Ibs.  per  square  inch,  to  a  volume  of  3  cubic  feet? 

Here,  no  heat  is  required  to  change  the  temperature  of 

the  air ;  all  is  used  in  doing  ex- 
ternal work. 


W=area  abed,  in  the  figure, 
=  P1F1  hyp.  log.  ~\ 

Ans.,  9180  ft.-lbs. 


17.  How  much  heat  in  ft.-lbs.  must  be  given  to  1.3 
cubic  feet  of  air  which  is  heated  at  constant  volume  from 
an  absolute  temperature  of  520  degrees  under  a  pressure 
of  2  Ibs.  per  square  inch,  to  an  absolute  temperature  of 
1000  degrees? 

Since  the  volume  is  kept  constant,  the  external  work  is 
zero  and 


w  =-^V»     Hence 
K  1± 

P  V  K 


_  _ 

-^     1.41-1     0.41' 


2X144X1.8  (1000-520),  ft 

520  X  0.41 
16 


242  STEAM    ENGINES    AND    BOILERS. 

.   18.    How  many  heat  units  are  given  to  the  air  in  Prob- 
lem 17?  Ans.,  1.08. 

19.  In  which  is  there  the  greater  amount  of  energy: 
1  Ib.  of  air  at  60  degrees,  under  a  pressure  of  100  Ibs.  per 
square  inch,  or  1  Ib.  of  air  at  60  degrees  under  a  pressure 
of   15  Ibs.  per  square  inch?     Give  the  reasons  for  your 
answer. 

20.  Given  a  quantity  of  air  whose  volume  is  3  cubic  feet 
at  60  degrees  under  a  pressure  of  45  Ibs.  per  square  inch. 
What  is  the  volume  and  temperature  of  this  air  after  it  is 
expanded   adibatically   until   its.  pressure   is    15   Ibs.    per 
square  inch? 

I  V  =  6.54  cub.  ft. 

[  7  =  378.6;  and  *=-82.4. 

21.  (a)  What  is  the  work  done  during  the  expansion  in 
Problem  20?     (b)  What  is  the  heat,  in  heat  units,  con- 
verted into  work? 

j  (a)   13,170  ft.-lbs. 
'"  (  (b)   16.9  heat  units. 

22.  Given  a  quantity  of  air  whose  volume  is  2  cubic 
feet  at  a  temperature  of  60  degrees  under  a  pressure  of 
80  Ibs.  per  square  inch,     (a)  What  is  the  weight  of  the 
air?     (b)  What  will  be  the  temperature  and  pressure  if 
the   air  be   expanded   adibatically  until  its  volume  is   8 
cubic   feet?      (c)    How   much   work   will   be   done   during 
this  expansion?      (d)  How  much  work  will  be. done  if  the 
air  be  expanded  isothermally  until  its  volume  is  8  cubic 
feet? 

Ans.,  (a)  0.83  Ibs.     (b)  -166  degrees  and  11.3  Ibs.  per 
sq.  in.     (c)  24,450  ft.-lbs.     (d)  32,000  ft.-lbs. 

23.  (a)  What  is  the  temperature  of  the  steam  in  a  boiler 


PROBLEMS.  243 

whose  gauge  pressure  is  90  Ibs.?     (b)  What  is  the  weight 
of  one  cubic  foot  of  the  steam?  j  (a)   330.9  degrees. 

'*  |  (b)  0.238  Ibs. 

24.  How  many  heat  untis  are  required  to  heat  16  Ibs. 
of  water  from  an  initial  temperature  of  60  degrees  and 
evaporate  it  under  a  pressure  of  30  Ibs.  by  the  gauge? 

Ans.,  18,200. 

25.  The  temperature  of  the  water  entering  a  boiler,  in 
which  the  gauge  pressure  is  60  Ibs.  per  square  inch,  is  the 
same  as  the  temperature  of  the  steam  in  the  boiler,     (a) 
What  is  the  external  work  done  in  evaporating  one  pound 
of  water?     (b)  What  is  the  internal  work  done  in  evapo- 
rating one  pound  of  water?  .         (  (a)     62,300  ft. -Ibs. 

5'  I  (b)    636,600  ft.-lbs. 

26.  Given  a  quantity  of  air  whose  temperature   is  80 
degrees;  whose  pressure  is  100  Ibs.  per  square  inch;    and 
whose  volume  is  2.2  cubic  feet.    It  is  made  to  pass  through 
the  following  Carnot  cycle:    It  is  expanded  isothermally 
until  its  volume  is  4.0  cubic  feet;    then  expanded  adia- 
batically  until  its  temperature  is  30  degrees;    then  com- 
pressed isothermally;  and'finally  it   is  compressed  adibat- 
ically  until   its    volume,  pressure,  and  absolute  tempera- 
ture are  the  same  as  at  the  beginning  of  the  cycle,     (a) 
What  is  the  total  quantity  of  heat,  H,  given  to  the  air? 
(b)  What  is  the  heat,  U,  taken  from  the  air?     (c)  What 
is  the  work,  W,  done  during  the  cycle?     (d)  What  is  the 
efficiency,  E,  of  the  cycle? 

H=  Pt  Vi  hyp.  log.  pS-  19,000  ft.-lbs. 

U  -  P,V,  hyp.  log.  £  =  Pl  ft  TZ  hyp.  log.  £ 

V  4  *  1  V I 

=  17,300  ft.-lbs. 
W=H—  [7=1,700  ft.-lbs. 

E  =  ^=Z>zl?=  0.093. 
ti         l 


244-  STEAM    ENGINES    AND    BO-ILERS. 

27.  One  pound  of  air  is  made  to  pass  through  the  fol- 
lowing cycle:  It  is  expanded  at  constant  pressure;  then 
expanded  isothermally;  then  compressed  at  constant 
pressure;  and  then  compressed  isothermally  until  the 
cycle  is  completed.  What  are  the  expressions  for  H,  U, 
and  E? 

The  work  diagram  is  shown 
in  the  figure.  Let  the  co-or- 
dinates of  a  be  Vlf  Plt  7\;  of 
b  be  I/2,  Plt  T2;  of  c  be  F3, 
P2,  72;  and  of  d  be  F4,  P2,  7\. 

During  the  expansion  from 
a  to  b  the  heat  given  to  the 
pound  of  air  is  Kv  (T2 — 7\)  + 
Pl  (V2 — Vj)',  and  during  the 
expansion  from  b  to  c  the  heat  given  to  the  air  is 

PI  V2  hyp.  log.  ~.    Adding  these  expressions  we  have  that 

"2 

the  total  heat,  H,  given  to  the  air  is 

H  =  K,  (T2-  TO  +Pl  (V2-VJ  +P,  V2  hyp.  log.  ^ 

2 

p  (V V  }  P 

__-tlV^2  *•'     \      T>     /T7  T7  \    i     T)     T7     ?„„.>,      7^^     *    1 

r— i 

PI  (F2— FO  r 


During  the  compression  from  c  to  d  the  heat  taken  from 
the  air  must  be  the  same  that  would  be  put  into  it  during 
expansion  from  d  to  c,  or  Kv  (T2 — 7\)+P2  (V3 — F4);  and 
the  heat  taken  from  the  air  during  compression  from  d  to  a 
is 

Pl  VJL  hyp.  log.  ~.     Therefore,   the   heat,    17,   taken   from 

the  air  is 

V-  K-T(r,— T.)  +pt(V,—VJ+P1  V.hyp.log.^. 

.  log.  &. 
- 


PROBLEMS.  245 

Since  P2  V3  =  Pl  V2,  and  P2  V,  =  Pl  Vlt  we  have 

P,(V9—V4)^Pl(V9—Vl)'t    and 

p  (Y  _  y  \  p 

V-     '(r     .        +pi  (Vf-V^+P,  V,  hyp.  log.  £ 

/  ^2 

-  Pl  (^~Fl)  r  +  P,  V.  hyp.  log.  £ 

r    L  ^2 

W-  H—U=Pl  (V—VJ  hyp.  log.  ^ 

^2 
W 


28.  If  in  Problem  27,  the  weight  of  air  used  is  0.25  Ib.  ; 
Pl  is  11,520  Ibs.  per  square  foot;  P2  is  2,200  Ibs.  per  square 
foot;  Y!  is  0.61  cubic  foot;  and  V2  is  2  cubic  feet;,  what 
will  H,  U,  W,  and  E  equal? 

Since  the  expressions  derived  for  H,  U,  W,  and  E,  in- 
volve only  the  pressures  and  volumes  of  the  gas,  the 
weight  need  not  be  considered.  Substitute  the  values  of 
Plt  Vj,  and  P2  in  the  expressions  for  H,  U,  W,  and  E  and 
get:  H  =  93,300;  U=  66,700;  W  =  26,600;  and  £  =  0.285. 

29.  Find  the  expressions  for  H,  U,  W,  and  E,  for  one 
pound  of   air  working  according  to  the  following  cycle: 
It  is  heated  at  constant  volume;  then  expanded  adiabati- 
cally;  then  compressed  at  constant  pressure  to  its  initial 
condition. 

The  work  diagram  is  shown  in  the  figure.  The  co-ordi- 
nates of  a  are  Plt  Vlt  7\;  of  6,  P2,  Vlt  T2;  and  of  c,  Plt 
V2,  TV 

During  the  change  from  a  to 
b  the  air  is  heated  at  constant 
volume,  no  work  is  done,  and  the 
heat  put  in  during  this  change  is 
/YV  (T2  —  7\).  During  the  change 
from  b  to  c  no  heat  is  either  given 
to,  or  emitted  by,  the  air.  Dur- 
v  ing  the  change  from  c  to  a  the 


246  STEAM    ENGINES    AND    BOILERS. 

same  amount  of  heat  is  taken  from  the  body  that  must  be 
given  to  it  for  a  change  from  a  to  c,  or, 


Therefore  we  have 

TT      i<r   (T      T  \         l  \    2         *•' 
ri  =  Kv(l2  —  li)  =  -        —  j— 

T  —  L 

t/=/C  (T—TJ  +P,  (V—VJ, 


W=H—  U. 

W 
E-IJJ. 

30.  In  Problem  29  let  Pt  be  15  Ibs.  per  square  inch;  P2 
be  80  Ibs.  per  square  inch;  Vl  be  1.3  cubic  feet;  and  V2  be 
4.26.     Find  the  values  of  H,  U,  W,  and  E. 

#  =  29,700;  £7=22,000;  ^=7,700;  and  £  =  0.26. 

31.  Deduce  the  expressions  for  H,   U,  and  W  for  one 
pound   of   air  for  the  following  cycle:  Air  expanded   at 
constant   pressure,    Plf    from    Vl   to    V2;   then   expanded 
adiabatically  from  V2  to  F3;  then  compressed  at  constant 
pressure,   P2,  from   V3  to   V4\  then  compressed  adiabati- 
cally to  its  initial  condition. 


r-i 


32.   In  Problem  31,  let  Pt  be  12,000  Ibs.  per  square  foot; 
P2  be  3,000  Ibs.  per  square  foot;  Vl  be  0.8  cubic  foot;  and 


PROBLEMS.  247 

V3  be  3.2  cubic  feet;  and  determine  the  values  of  H,   U9 
W,  and  E. 

#  =  99,000;   £7  =  66,200;   VT  =  32,800;  and  £=0.33 

33  Determine  the  horse-power  of  a  double-acting 
engine  whose  cylinder  is  13  inches  in  diameter  and  which 
has  an  18-inch  stroke,  when  making  220  revolutions  per 
minute  while  taking  steam  at  80  Ibs  by  the  gauge  and 
cutting  off  at  \  stroke.  Neglect  the  clearance  and  as- 
sume that  the  mean  back  pressure  is  20.5  absolute. 

Ans.,  96.7  horse-power. 

34.  An  engine  has  a  clearance  volume  which  is  0.08  of 
the  volume  swept  through  by  the  piston  per  stroke.     If 
the  steam  be  cut  off  at  £  stroke,  what  will  be  the   num- 
ber of  times  it  is  expanded?  Ans.,  3.86  times. 

35.  Assume   that   the  mean   back  pressure  is    19   Ibs. 
absolute,  and  that  the  clearance  volume  is  10  per  cent,  of 
the  volume  swept  through  by  the  piston  per  stroke;  and 
determine  the  horse-power  developed  by  a  double-acting 
engine,  whose  cylinder  is  12  inches  in  diameter  and  has 
a  14-inch  stroke,  when  making  260  revolutions  per  minute, 
while  taking  steam  at  70  Ibs.  by  the  gauge  and  cutting  off 
at  |  stroke.  Ans.,  97  horse-power. 

36  What  is  the  weight  of  the  steam  used  per  stroke 
by  the  engine  in  Problem  33?  Ans.,  0.075  Ibs. 

37.  Neglect  the  clearance  volume  of  the  engine  in 
Problem  35,  and  determine  the  weight  of  steam  used  per 
hour  per  indicated  horse-power  Ans.,  22.8  Ibs. 

On  account  of  the  loss  by  condensation  and  other  causes, 
the  weight  of  steam  actually  used  per  hour  per  indicated 
horse-power  will  be  from  \  to  J  greater  than  22.8  Ibs.,  or 
between  27  and  31  pounds 


248  STEAM    ENGINES    AND    BOILERS. 

38.  Assume  that  the  temperature  of  the  water  entering 
the  boiler  is  150  degrees,  and  determine  the  efficiency  of 
the  steam  in  Problem  33.  Ans.,  £  =  0.117 


39.  If  it  were  possible  to  use  the  steam  in  a  perfect 
engine,  working  according  to  the  Carnot  cycle,  between 
the  same  limits  of  temperatures  as  in  Problem  38,  what 
would  the  efficiency,  be?  Ans.,  0.22. 


40.  The  cylinders  of  a  locomotive  are  19  inches  in 
diameter  and  have  a  24-inch  stroke;  the  driving  wheels 
are  7  feet  in  diameter;  and  the  mean  back  pressure  against 
which  the  pistons  work  is  19  Ibs.  absolute.  Determine 
the  horse -power  developed  by  the  locomotive  when  taking 
steam  at  150  Ibs.  by  the  gauge  and  cutting  off  at  f  stroke, 
while  traveling  at  a  speed  of  40  miles  per  hour. 


The  number  of  revolutions  made  per  minute  by  each 
driving  wheel  is  equal  to  the  number  of  feet  in  one  mile, 
5,280,  multiplied  by  the  number  of  miles  traveled  per 
hour,  and  divided  by  60  times  the  circumference  of  one 

,  .   .  5280X40  ^ 

dnvmg  wheel,  ^n        IAW  =  l^O.          Horse-power  =  1458. 
OU  X  o. 


41.  Assume  the  mean  effective  pressure  to  be  40  Ibs., 
the  number  of  revolutions  to  be  75  per  minute,  and  the 
length  of  stroke  to  be  42  inches;  and  detemine  the  dia- 
meter of  the  cylinder  of  a  double-acting  engine  which 
will  develop  200  horse-power.  Diameter  =  20  inches. 


42.  If  the  mean  back  pressure  is  20  Ibs.  absolute,  how 
many  times  must  steam  at  an  initial  pressure  of  80  Ibs. 
by  the  gauge,  be  expanded  in  order  that  the  mean  effect- 
ive pressure  shall  be  40  Ibs.? 


PROBLEMS.  249 

Here  we  have 


hyp.  l°g>  r  =  0.632  r—l. 

In  order  to  solve  this  we  must  assume  various  values  of  r 
and  try  them  in  the  equation,  we  shall  finally  get  a  value 
of  r  that  will  satisfy  it. 

If  r=     3,  hyp  log.  r=1.10;  and  we  have  1.10>  1.89-1 

"    r=     4,     "     "       =1.39;  "     1.39<2.52-1 

"    r  =  3.5,     "     "       =1.25;  "            "     1.25>2.21-1 

"    r  =  3.6,     "     "       =1.28;  "     1.28>2.27-1 

"    r  =  3.7,     "     "       =1.31;  "     1.3K2.34-1 
r  is  equal  to  3.6,  about. 

43  About  how  many  revolutions  per  minute  should  be 
made  by  an  automatic  high  speed  engine  whose  stroke  is 
18  inches?  Ans.,  218. 

44.  About  what  should  be  the  diameter  of  the  cylinder 
of   an    automatic   high-speed   engine   whose   stroke   is    16 
inches?  Ans.,  12  inches. 

45.  About  what  should  be  the  length  of  the  connecting 
rod  of  an  automatic  high-speed  engine  whose   stroke   is 
14   inches?  Ans.,  35  inches. 

46.  About  how  many  revolutions  per  minute  should  be 
made  by  a  Corliss  engine  whose  stroke  is  42  inches? 

Ans.,  67. 

47.  About  what  should  be  the  diameter  of  the  cylinder 
of  a  Corliss  engine  whose  stroke  is  36  inches? 

Ans.,  18  inches. 

48.  About  what  should  be  the  length  of  the  connecting 
rod  of  a  Corliss  engine  whose  stroke  is  54  inches? 

Ans.,  162  inches. 

49.  How  does  increasing  the  angle   of  advance  affect 


250  STEAM    ENGINES    AND    BOILERS. 

the  lead,  the  point  of  cut-off,  and  the  point  of  compression? 

50.  Through  what  distance  will  the  valve  move,  if  the 
eccentric  be  turned  through  an  angle  equal  to  the  angle 
of  advance? 

51.  What  must  be  done  to  make  the  cut-off  occur  later, 
on  a  single-valve  engine,  and  not  change  the  point  of  re- 
lease or  the  point  of  compression  ? 

52.*  Find  the  steam  lap  and  the  lead  of  a  valve,  whose 
travel  is  4J  inches,  that  admits  steam  when  the  piston  is 
yij-g-  of  the  stroke  before  the  beginning  of  the  forward 
stroke,  and  that  cuts  off  at  $•  of  the  stroke. 

Ans.,  Lap=  1J  in.; 


53.  Find  the  steam  lap  and  the  lead  of  a  valve,  whose 
travel  is  4£  inches,  that  admits  steam  when  the  piston  is 
iff  of  the  stroke  before  the  beginning  of  the  forward  stroke  , 
^nd  that  cuts  off  at  £  of  the  stroke. 

Ans.,  Lap=  IJf  in.;   lead  =  T5T  in. 

54.  Steam  is  admitted  when  the  piston  is  at  the  begin- 
ning of  the  stroke  and  is  cut  off  at  J  of  the  stroke,  by   a 
valve  whose  steam  lap  is  2J  inches.     Find  the  lead,  the 
eccentricity,  and  the  angle  of  advance. 

Ans.,  Lead=0;    eccentricity  =  3  in.;    angle    of    advance 
=  45°. 

55.  Steam  is  admitted  when  the  piston  is   -jj-j  of  the 
stroke  before  the  beginning  of  the  forward  stroke,  and  is 
cut  off  at  J  of  the  stroke,  by  a  valve  whose  steam  lap  is 
1T\  inches.    Find  the  lead,  the  eccentricity,  and  the  angle 
of  advance. 

Ans.,  Lead  =  /3-  in.;    eccentricity  =  If  in.;    angle  of  ad- 
vance =  63°-  15'. 

56.  Steam  is  admitted  when  the   piston  has  made  yj-g  of 


*In  working  the  valve  diagram    problems  it  will  be  well  to 
make  the  crank  circle  8  inches  in  diameter. 


PROBLEMS. 


251 


the  stroke,  and  is  cut  off  at  -fy  of  the  stroke,  by  a  valve 
whose  lead  is  -  -fa  of  an  inch.  Find  the  steam  lap  and  the 
eccentricity.  Ans.,  Lap  =  If  J  in.;  eccentricity  =  2^|  in. 

There  are  some ,  special  cases  where  the  construction 
shown  in  Fig.  45  fails,  and  other  constructions  must  be 
used.  The  most  common  case  that  occurs  is  when  the  line 
eh  is  so  nearly  parallel  to  ef  that  it  is  impossible  to  deter- 
mine with  any  accuracy  their  point  of  intersection,  O' .  In 
such  cases  the  construction  must  be  exactly  the  same  as 
for  Fig.  45  until  the  point  h  is  fixed,  then  instead  of  draw- 
ing the  line  eh  draw  kg,  as  shown  in  Fig.  45a.  Then  draw 
dk  through  d  parallel  to  hg,  and  continue  it  until  it  cuts  fg 
prolonged  at  k.  Through  k  draw  O'k  cutting  Ob  at  6,  and 
efatO'.  O'b  is  the  steam  lap.  If  O'd  be  drawn,  the  angle 
it  makes  with  Ob  will  be  the  required  angle  of  advance. 
O'd  is  the  eccentricity. 

If  the  lead  be  zero,  the  points  0,  d,  and  e,  in  Figs.  45  and 
45a  will  coincide.  In  this  case  the  method  of  Fig.  45  fails 
but  the  method  shown  in  Fig.  45a  may  be  used  for  the 


FIG.  45a. 


252 


STEAM    ENGINES    AND    BOILERS. 


solution  of  the  problem.     Sometimes  it  is  preferable  to  use 
the  following  method,  indicated  by  Fig.  456:    Since     he 


lead  is  zero  we  know  that  the  crank  is  in  the  position  OA1 
in  Fig  456  when  the  steam  is  admitted.  Let  OB  represent 
the  position  of  the  crank  at  cut-off.  Now  we  know  that 
the  center  of  the  eccentric  is  somewhere  on  the  line,  OD, 
bisecting  the  angle  BOAl.  Assume  any  point,  a,  as  a  trial 
center  of  the  eccentric;  and  draw  the  valve  circle  aeO. 
With  O  as  a  center  draw  the  lap  circle  em,  cutting  Oa  at  m. 
If  Oa  were  the  eccentricity  and  Oe  the  steam  lap,  the 
maximum  opening  of  the  valve  would  be  am.  But  am  = 
Oa— Om  =  Oa—Oe  =  Oa  ( I— cos  DO  A ) .  Since  the  angle 
DO  A,  is  constant,  we  see  that  the  maximum  opening  of 
the  valve  is,  in  this  case,  directly  proportional  to  the 
eccentricity.  Therefore,  make  Od  equal  to  ma;  and  Oh 
equal  to  the  required  maximum  opening.  Draw  da;  then 
draw  ha'  parallel  to  da  and  cutting  Oa  at  a'.  Oa'  is  the 
required  eccentricity.  Through  a'  draw  a  line  perpendicu- 
lar to  OA,  and  cutting  it  at  ef.  Oe'  is  the  required  steam 
lap. 

In  Problem  57  the  student  may  use  the  regular  construc- 
tion shown  in  Fig.  45  or  the  construction  shown  in  Fig.  45a. 
In  Problem  58  the  regular  construction  fails,  and  the  con- 
struction shown  in  Fig.  45a  or  that  in  Fig.  456  must  be 
used.  In  Problem  59  it  will  probably  be  best  to  use  the 
construction  shown  in  Fig.  45a. 


PROBLEMS.  253 

57.  Steam  is  cut  off  at  f  of  the  stroke  by  a  valve  whose 
maximum  opening  is  }  of  an  inch,  and  whose  lead  is  J  of 
an  inch.     Find  the  steam  lap,  the  eccentricity,  and  the 
angle  of  advance. 

Ans.,   Lap=l  in.;    eccentricity  =  1J  in.;    angle   of   ad- 
vance =  40°. 

58.  Steam  is  cut  off  at  \  of  the  stroke  by  a  valve  whose 
maximum  opening  is  f  of  an  inch,  and  whose  lead  is  —  T1^ 
of  an  inch.    Find  the  steam  lap  and  the  eccentricity 

Ans.,  Lap=  1T\  in.;  eccentricity  =  2^  in. 


59.  Steam  is  cut  off  at  \  of  the  stroke  by  a  valve  whose 
maximum  opening  is  £  inch,  and  whose  lead  is  zero.     Find 
the  steam  lap,  and  the  eccentricity 

Ans.,  Lap  =  3^2  in.;  eccentricity  =  3|J  in. 

60.  The  sine  of  the  angle  of  advance  is  J|,  the  eccen- 
tricity is  2J  inches,  and  the  compression  begins  when  the 
piston  has  made  -fj  of  the  return  stroke.    Find  the  exhaust 
lap  and  the  point  of  release. 

Ans.,  Lap=lT\  in.;    release  begins  when  the  piston  is 
of  the  stroke  from  the  end  of  the  stroke. 


61.  The  sine  of  the  angle  of  advance  is  }£,  the  eccen- 
tricity is  2  inches,  and  the  point  of  compression  is  ^f  of 
the  stroke  from  the  beginning  ot  the  return  stroke.     Find 
the  exhaust  lap  and  the  point  of  release. 

Lap=l55£  in.;   release  begins  when  the  piston  is  TJ^  of 
the  stroke  from  the  end  of  the  forward  stroke. 

62.  The  point  of  release  is  Tf  ff  of  the  stroke  before  the 
end  of  the  forward  stroke,  compression  begins  at   T\  of 
the  return  stroke,  and  the  eccentricity  is  3£  inches.     Find 
the  exhaust  lap  and  the  angle  of  advance. 

Lap  =1  }f  in.;  angle  of  advance  =  50°-45/. 


254  STEAM    ENGINES    AND    BOILERS. 

63.  Find  the  center  of  suspension  of  the  eccentric  of 
an  automatic  high-speed  engine  on  which  the  cut-off 
changes  from  |  to  f  of  the  stroke,  and  the  maximum 
opening  of  the  valve  when  cutting  off  ^  stroke  is  f  of  an 
inch.  The  lead  of  the  valve  shall  be  -fs  of  an  inch  positive, 
for  cut-off  at  J  the  stroke ;  zero,  for  cut-off  at  J  the  stroke ; 
and  T3F  of  an  inch  negative,  for  cut-off  at  f  of  the  stroke. 


64.  For  an  indicator  pendulum  motion,  such  as  is  shown 
in  Fig.  52,  what  should  be  the  shortest  lengths  of  the 
distances  Be  and  BD  in  order  to  get  a  card  3  inches  long 
from  an  engine  whose  stroke  is  18  inches? 

Ans.,  Bc  =  36in. 


65.  The  indicator  card  taken  from  an  engine  whose 
cylinder  is  13  inches  in  diameter  and  which  has  a  stroke 
of  21  inches,  is  3r3^  inches  long,  and  has  an  area  of  1.46 
square  inches.  What  was  the  horse-power  developed  by 
the  engine  if  the  card  were  taken  with  an  80-lb.  spring 
while  the  engine  was  making  180  revolutions  per  minute? 

Ans.,  93  horse-power. 


66.  On  an  indicator  card  3^  inches  long,  taken  from 
an  engine  whose  cylinder  is  13  inches  in  diameter  and 
whose  stroke  is  21  inches,  the  length  of  the  line  corre- 
sponding to  the  line  fg  in  Fig.  58  is  2f  inches.  If  the 
pressure  corresponding  to  the  point  /,  in  Fig.  58,  be  13  Ibs. 
per  square  inch  by  the  gauge,  what  is' the  weight  of  steam 
used  per  stroke  by  the  engine?  Ans.,  0.0825  Ibs. 


67.  If  the  engine  from  which  the  card  in  Problem  66  is 
taken,  develop  93  indicated  horse-power  when  making  180 
revolutions  per  minute,  what  is  the  weight  of  steam  used 
per  hour  per  indicated  horse-power?  Ans.,  19.1  Ibs. 


PROBLEMS.  255 

68.  Assume  c  in  (63)  to  be  0.85;  E  in  (64)  to  be  9;  Pl 
to  be  105  Ibs.,  by  the  gauge;  P3  to  be  8  Ibs.  absolute;  the 
length  of  the  stroke  to  be  20  inches;  the  number  of  revo- 
lutions to  be  200  per  minute;  and  the  ratio  of  the  volume 
of  the  low-pressure  cylinder  to  that  of  the  high-pressure 
cylinder  to  be  3;  and  determine  the  diameters  of  the  cyl- 
inders of  a  compound-engine  to  develop  200  horse-power. 

Diameter  of  low  pressure  cylinder  =  20.7  in. 
"          "  high        "  "       =  12.0  in. 

69.  How  many  times  is  the  steam  expanded  in  the  high 
pressure  cylinder  in  Problem  68?  Ans.,  3  times. 

70.  An  engine  takes  steam  at  an  initial  pressure  of  80 
Ibs.   by  the  gauge  and  expands    it    3.7    times    against  a 
mean  back  pressure  of  18  Ibs.  absolute.    How  much  would 
the  horse-power  of  the  engine  be  increased  by  the  use  of 
a  condenser  which  reduces  the  mean  back  pressure  to  6 
Ibs.  absolute  ?  Ans.,  29  per  cent. 

71.  To  what  could    the   number  of  expansions  of  the 
steam  in  the  engine  of  Problem  70  be  changed,   and  the 
engine  continue  to  do  the  same  work  with  the  condenser 
that  it  did  without? 

From  (68)  we  have 

1  +  jiypm  log,  r  _  1  +  hyp,  log.  3.7       18-6  _ 
"          ~~  ~~- 


Therefore,  we  have 

hyp.  log.  r  =  0.50r-.l 
If 


r  =  3         we  ha 
r  —  5 
r  =  6          "       ' 
r=5.5      " 
r=5.4       " 
r=5.3       " 
r  =  5.4,  about. 

ve  1.10>  1.50  —  1 
1.61>2.50—  1 
1.79  <3.  00-1 
1.70<2.75-1 
1.69<2.70  —  1 
1.67>2.65-1 

256  STEAM    ENGINES    AND    BOILERS. 

72.  To  what  could  the  boiler  pressure  of  the  steam  in 
Problem  70  be  reduced,  and  the  engine  continue  to  do  the 
same  work  with  the  condenser  that  it  did  without? 

Ans.,  about  65  Ibs.  by  the  gauge. 

73.  If  the  condensing  water  enters  the  condenser  at 
70  degrees  and  leaves  it  at  110  degrees,  how  many  pounds 
of  water  will  be  required  to  condense  one  pound  of  steam 
exhausted  from  the  engine  in  Problem  70? 

Ans.,  26.9  Ibs. 

74.  About  what  is  the  vacuum,  in  inches,  of  Mercury, 
maintained  by  the  condenser  in  Problem  70? 

Ans.  We  may  say  that,  roughly,  the  difference  between 
the  pressure  against  which  the  steam  is  exhausted  without 
and  with  the  condenser  is  equal  to  the  difference  between 
the  mean  back  pressures  without  and  with  the  condenser, 
or  to  18 — 6=12  Ibs.  That  is,  the  pressure  in  the  con- 
denser is  12  pounds  less  than  atmospheric  pressure,  or  is 
only  3  Ibs.  absolute.  This  corresponds  to  a  vacuum  of 
12X2  =  24  inches. 

75.  Calculate  the  factor   of  evaporation  for   a  gauge 
pressure  of  75  Ibs.  and  an  initial  temperature  of  the  feed 
water  of  135  degrees. 

76.  A  boiler  evaporates  5000  Ibs.   of  water  per  hour 
from  an  initial  temperature  of  145  degrees,  and  under  a 
pressure  of  80  Ibs.  by  the  gauge.     What  is  the  equivalent 
water  evaporated  per  hour  from  and  at  212  degrees? 

*Ans.,  5515  Ibs. 

77.  What  is  the  boiler  horse-power  of  a  boiler  which 
evaporates  3080  Ibs.   of  water  per  hour  from  an  initial 
temperature  of  135  degrees  and  under  a  pressure  of  100 
Ibs.  by  the  gauge?  Ans..  100. 

78.  A  boiler  evaporates  3500  Ibs.   of  water  per  hour 
from  an  initial  temperature  of  120  degrees  and  under  a 


PROBLEMS.  257 

pressure  of  80  Ibs.  by  the  gauge;  a  second  boiler  evap- 
orates 4000  Ibs.  of  water  from  an  initial  temperature  of 
110  degrees  and  under  a  pressure  of  60  Ibs.  by  the  gauge. 
Which  of  the  two  boilers  utilizes  the  greater  amount  of 
heat  per  hour? 

79.  Calculate  the  number  of  heat  units  evolved  by  the 
complete  combustion  of  one  pound  of  coal  which  con- 
tains 69.8  per  cent,  of  carbon;  5.26  per  cent,  of  hydrogen; 
and  8.35  per  cent,  of  oxygen. 

Ans.,  12,750  heat  units. 

•  80.  Calculate  the  number  of  heat  units  evolved  by  the 
complete  combustion  of  one  pound  of  petroleum  which 
contains  84.9  per  cent,  of  carbon;  13.7  per  cent,  of  hy- 
drogen; and  1.40  per  cent,  of  oxygen. 

Ans.,  20,700  heat  units. 

81.  How  many  pounds   of  water   can   be   evaporated 
from  and  at  212  degrees  by  the  heat  evolved  by  the  com- 
plete combustion  of  one  pound  of  coal  containing  65.2 
per  cent,  of  carbon;   4.92  per  cent,  of  hydrogen;   and  8.64 
per  cent,  of  oxygen?  Ans.,  12.65  Ibs. 

82.  Assume  that   one  cord  of  wood  weighs  3000  Ibs. 
and  that  each  pound  of  wood  will  evolve  5000  heat  units 
when  completely  burned,  and  determine  when  it  is  cheaper 
to  buy  wood  than  to  buy  the  coal  in  Problem  81. 

Cheaper  to  buy  wood  as  long  as  one  ton  (2000  Ibs.)  of 
coal  costs  more  than  1.57  as  much  as  one  cord  of  wood. 

83.  If  40  per  cent,  of  the  heat  evolved  by  the  combus- 
tion of  each  pound  of  the  coal  in  Problem  79  is  lost,  how 
many  pounds  of  coal  will  be  required  to  evaporate  5650 
Ibs.  of  water  from  an  initial  temperature  of  130  degrees 
and  under  a  pressure  of  80  Ibs.  by  the  gauge? 

Ans.,  800  Ibs: 
17 


258  STEAM    ENGINES    AND    BOILERS, 

84.  Suppose  that  in  burning  the  coal  in  Problem  81  it 
is  found  that  one-half  only  of  the  carbon  is  completely 
burned,  and  that  the  other  half  is  burned  to  carbon  mon- 
oxide ;  what  is  the  heat  evolved  per  pound  of  coal  burned  ? 

Ans.,  8540  heat  units. 

85.  How  many  pounds  of  air  are  required  for  the  com- 
plete combustion  of  one  pound  of  coal  containing  79.65 
per  cent,  of  carbon,  5.58  per  cent,  of  hydrogen,  and  4.64 
per  cent,  of  oxygen?  Ans.,  11.4  Ibs. 

86.  Assume  that  20  Ibs.  of  .air  at  60  degrees  are  ad- 
mitted to  a  furnace  for  each  pound  of  the  coal  in  Problem 
85  that  is  burned;  that  the  specific  heat  of  the  gases  in 
the  chimney  is  0.24;    and  that  the    temperature    of    the 
escaping  gas  is  430  degrees  ;   and  determine  the  number  of 
heat  units  carried  off  by  the  gases  per  pound  of  coal  burned. 

All  the  carbon,  hydrogen,  and  oxygen  in  the  coal  that 
is  burned  is  carried  up  the  chimney.  Therefore,  the  weight 
of  the  gases  carried  up  the  chimney  per  pound  of  coal  burned 
is  the  weight  of  the  air  admitted  per  pound  of  coal  plus 
the  weight  of  the  combustible  and  volatile  matter  in  the 
coal,  or  it  is  20  +  0.7965  +  0.0558  +  0.0464,  equal  20.9  Ibs. 
Heat  carried  off  =1850  units. 

87.  Determine   the   area  of  the   heating   surface   of  a 
return  tubular  boiler  66  inches  in  diameter,   16  ft.  long, 
and  containing  98  tubes  each  3  inch  in  diameter,  that  is 
set  so  that  §  of  the  -circumference  of  its  shell  is  exposed 
to  the  hot  gases.  Ans.,  1414  sq.  ft. 

88.  What  would  be  the  area  of  the  heating  surface  of 
the  boiler  in  Problem  87  if  it  were  set  so  that  but  £  of  the 
shell  was  exposed  to  the  hot  gases?  Ans.,  1368  sq.  ft. 


89.  Assume  12£  sq.  ft.  of  heating  surface  per  boiler 
horse-power,  and  determine  the  horse-power  of  the  boilers 
in  Problem  87  and  88. 


PROBLEMS. 


259 


90.  Assume  k  in  (90)  to  be  J,  and  determine  what  will 
be  the  velocity  of  the  gases  in  a  chimney  120  ft.  high, 
when  the  temperature  of  the  gases  is  450  degrees  and  that 
of  the  air  is  65  degrees.  Ans.,  25  ft.  per  second. 


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